Freezing- Point,   Be iling- Point, 


' HPTI  v7 1T"V   MPT -. 

•Jul.l  v  ii  !     j*M;.;l  i. 


HARRY  C   JOHKS. 


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REESE  LIBRARY 

OF  TIU-: 

UNIVERSITY  OF  CALIFORNIA. 


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Accession  No. 


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...THE... 

Freezing-Point,  Boiling-Point, 


-AND 


Conductivity  Methods 


— BY — 


HARRY    C.  JONKS, 

INSTRUCTOR  IN  PHYSICAL  CHEMISTRY  IN  JOHNS 
HOPKINS  UNIVERSITY 


EASTON,  PA.: 
CHEMICAL   PUBLISHING  CO. 

1897 

(All rights  reserved.} 


COPYRIGHT,  1897,  BY  HOWARD  HART. 


PREFACE 

I  have  been  impressed,  in  teaching  the  physical  chem- 
ical methods  in  the  laboratory,  with  the  fact,  that  there 
is  no  readily  accessible  place  in  which  they  are  treated 
satisfactorily  from  both  the  standpoint  of  theory  and  of 
practice.  In  the  text-books,  the  theoretical  side  is  de- 
veloped, and  usually  without  sufficient  attention  to  the 
details  of  manipulation,  to  enable  them  to  be  applied 
successfully  in  the  laboratory.  In  the  laboratory  man- 
uals, on  the  other  hand,  these  methods  are  often  treated 
largely  from  the  mechanical  side,  and  their  theoretical 
bearing  might  thus  be  lost  sight  of. 

The  physical  chemical  methods,  which  find  most  fre- 
quent application  in  the  laboratory,  are  probably  those 
based  upon  the  lowering  of  the  freezing-point,  and  the 
rise  in  the  boiling-point  of  a  solvent,  produced  by  a  dis- 
solved substance,  and  the  electrolytic  conductivity  of 
solutions  of  electrolytes.  It  is  my  chief  object  in  pre- 
paring this  little  work  to  give  an  account  of  the 
operations  involved  in  carrying  out  these  methods  in 
the  laboratory.  But  since  the  mere  mechanical  applica- 
tion of  any  scientific  method  is  a  matter  of  comparatively 
little  significance,  I  have  aimed  to  give,  also,  enough  of 
the  theoretical  ground  on  which  each  of  them  rests,  to 
enable  the  student  to  work  with  them  intelligently,  and 
to  see  clearly  their  scientific  significance  and  use. 

HARRY  C.  JONES. 


CONTENTS 


PART  I 
THE  FREEZING-POINT  METHOD 

PAGE 

Theoretical  Discussion i 

Early  History I 

Work  of  Raoult i,  2 

Molecular  Lowering  for  Different  Solvents 3 

Molecular  Lowering  in  Aqueous  Solutions 4 

Theory  of  Electrolytic  Dissociation 5 

Calculation  of  the  Molecular  Lowering 6,  7 

Experimental  Verification 8 

Calculation  of  Molecular  Weights  from  Lowering  of  Freez- 
Point 8,  9 

The  Application  of  the  Freezing-Point  Method  to  the  Determina- 
tion of  Molecular  Weights  in  Solution 9 

The  Apparatus  of  Beckmann 10,  1 1 

Carrying  out  a  Determination    11-13 

Correction  for  the  Separation  of  Ice 13,  14 

The  Application  of  the  Freezing-Point  Method  to  the  Measure- 
ment of  Electrolytic  Dissociation 14 

The  Method  of  Calculating  Dissociation  from  Lowering  of 

Freezing-Point •. 15,  16 

The  Method  of  Work 16 

The  Apparatus  of  Jones 17,  20 

Comparison  of  the  Results  with  the  Dissociation  from  Con- 
ductivity Measurements 21 


PART  II 
THE  BOILING-POINT  METHOD 

PAGE 

Theoretical  Discussion 23 

Historical 23,  24 

Work  of  Raoult 24,  25 

The  Relative  Lowering  of  the  Vapor-Tension 26 

Calculation  of  Molecular  Weights  from  Lowering  of  the  Va- 
por-Tension     27 

Beckmann's  Work  on  Rise  in  Boiling-Point 27,  28 

Calculation  of  Molecular  Weights  from  Rise  in  the  Boiling- 
Point  of  Solvents 28 

Values  of  the  Constants  for  Solvents 29 

Relations  between  Boiling-Point  and  Freezing-Point  Meth- 
ods   29,  30 

The  Application  of  the  Boiling-Point  Method  to  the  Determina- 
tion of  Molecular  Weights  in  Solution 30 

The  Apparatus  of  Beckmann 3i~33 

The  Apparatus  of  Hite 33~35 

The  Apparatus  of  Jones 34-36 

Carrying  Out  a  Determination 36-39 

Correction  for  Separation  of  Vapor 39 

Results  of  Measurements 40,  41 

PART  III 

THE  CONDUCTIVITY  METHOD 

Two  Classes  of  Conductors 42 

Electrolytes  and  Non- Electrolytes 42 

Specific  Conductivity     43,  44 

Molecular  Conductivity 44 

Dissociation  Measured  by  Conductivity  Method 45,  46 

Determination  of  /*«   46-50 


CONTENTS  vii 

PAGE 

The  Application  of  the  Conductivity  Method  to  the  Measure- 
ment of  Electrolytic  Dissociation 50 

The  Apparatus  Employed 50-52 

Calculation  of  the  Molecular  Conductivity 52,  53 

Temperature  Coefficient  of  Conductivity 54 

The  Ostwald  Thermoregulator 55 

Calibrating  the  Wire 56-58 

Carrying  Out  a  Conductivity  Measurement 58 

Determination  of  the  Cell  Constant 59 

Precautions 60 

Correction  for  the  Conductivity  of  Water 60,  61 

The  Purification  of  Water 61-63 

Substances  to  be  Used 64 


PART  I 


THE  FREEZING-POINT  METHOD 


Theoretical 

It  has  long  been  known  that  when  a  solid  is  dissolved 
in  a  liquid,  the  freezing-point  of  the  solution  is  lower 
than  that  of  the  solvent.  The  first  quantitative  relation 
we  owe  to  Blagden,1  who  pointed  out  that  the  lowering 
of  the  freezing-point  of  water,  produced  by  different 
amounts  of  the  same  substance,  was  proportional  to 
the  amount  of  substance  present.  This  same  fact  was 
rediscovered  much  later  by  Riidorff.2  A  marked  ad- 
vance was  made  by  Coppet,3  who  dealt  with  comparable, 
rather  than  with  equal  amounts  of  different  substances. 
He  used  quantities  of  different  substances  which  bore  to 
one  another  the  same  relation  as  their  molecular  weights, 
and  found  that  such  quantities,  of  substances  which  are 
chemically  allied,  produce  very  nearly  the  same  lower- 
ing of  the  freezing-point  of  any  given  solvent.  In  a 
word,  the  lowering  of  the  freezing-point  of  a  solvent  by 
a  dissolved  substance,  is  proportional  to  the  number  of 
parts  of  the  substance  present. 

This  is  about  what  was  known  when  the  problem  was 
taken  up  by  Raoult,  and  it  is  to  him  more  than  to  any 
other  that  we  owe  the  present  development  of  the  freez- 
ing-point method.  He  investigated  water  solutions  of 
organic  compounds,  and  found  that  the  lowering  pro- 
duced by  molecular  quantities  was  very  nearly  a  con- 
stant. He  used  other  solvents,  such  as  benzene,  and 

1  Phil.  Trans.,  78,  277. 

2  Pogg.  Annalen,  114,  63;  145,  599. 

3  Ann.  chim.  phys.,  [4],  23,  366. 


2  THE   FREEZING-POINT   METHOD 

found  that  comparable  quantities  of  dissolved  substances 
produced  the  same  lowering  of  the  freezing-point.  His 
investigations  included  nitrobenzene,  ethylene  bromide, 
formic  and  acetic  acids,  and  in  each  solvent  a  large 
number  of  substances  were  dissolved.  He  was  thus  in 
a  position  not  only  to  compare  the  lowerings  produced 
by  different  substances  in  the  same  solvent,  but  the  low- 
erings in  different  solvents. 

As  the  result  of  this  work,  Raoult  attempted  the  fol- 
lowing generalization. 

One  molecule  of  any  complex  substance  dissolved  in 
one  hundred  molecules  of  a  liquid,  lowers  the  freezing- 
point  of  the  liquid  by  nearly  a  constant  amount,  which 
is  0.62°.  This  has  been  shown  not  to  hold  rigidly. 

When  a  gram-molecular  weight  of  any  substance  is 
dissolved  in  say  100  grams  of  a  solvent,  the  lowering  of 
the  freezing-point  of  the  solvent  is  a  constant,  regard- 
less of  the  nature  of  the  substance,  provided  that  there 
is  no  aggregation  of  the  molecules  of  the  substance,  and 
no  dissociation.  This  was  shown  to  hold  approximately 
for  a  large  number  of  substances,  and  for  several  solvents 
by  Raoult.1  The  molecular  lowering,  which  is  the  low- 
ering produced  by  a  gram-molecular  weight  of  the  sub- 
stance in  100  grams  of  the  solvent,  was  calculated  by 
him  thus  : 

If  g  grams  of  the  substance  are  dissolved  in  100  grams 
of  the  solvent,  if  m  is  the  molecular  weight  of  the  sub- 
stance, and  A  the  lowering  of  the  freezing-point  of  the 
solvent  produced  by  the  presence  of  g  grams  of  the  sub- 
stance, then  the  molecular  lowering  is  calculated  from 
the  formula : 

Molecular  lowering  =  -  — . 

o 
1  Ann.  chim.  phys.  [6J,  2,  66. 


THE    FREEZING-POINT   METHOD  3 

A  few  results  will  show  the  values  of  the  molecular 
lowering  for  different  solvents. 

SOLVENT,  ACETIC  ACID. 

Molecular 
lowering. 

Methyl  iodide 38.8 

Aldehyde 38.4 

Acetone ,, 38.1 

Benzoic  acid 43.0 

Ethyl  alcohol 36.4 

Acetamide 36. 1 

Stannic  chloride .  - 41.3 

Carbon  disulphide 35.6 

Sulphuric  acid  . '. 18.6 

Hydrochloric  acid 17.2 

SOLVENT,  BENZENE. 

Methyl  iodide 50.4 

Anthracene 51.2 

Ether 49.7 

Acetone 49.3 

Chloral 50.3 

Stannic  chloride 48.8 

Methyl  alcohol 25.3 

Ethyl  alcohol  . . . .  .\ 28.2 

Benzoic  acid 25.4 

SOLVENT,  WATER. 

Methyl  alcohol 17.3 

Cane-sugar 18.5 

Acetamide 17.8 

Chloral  hydrate 18.9 

Milk-sugar 18.  i 

Acetone 17.1 

Hydrochloric  acid 39.1 

Nitric  acid 35.8 

Sulphuric  acid 38.2 

Sodium  hydroxide 36.2 

Potassium  chloride 33.6 


4  THE   FREEZING-POINT   METHOD 

A  careful  study  of  these  results  will  bring  out 
some  interesting  facts.*"  The  value  of  the  molecular 
lowering  of  acetic  acid  and  of  benzene  is  very  nearly  a 
constant  for  each  solvent.  This  is  true  for  a  large  num- 
ber of  substances  of  the  general  type  of  most  of  those  given 
above,  i.  e.,  non-electrolytes.  There  are,  however,  ex- 
ceptions for  these  solvents.  In  the  case  of  acetic  acid, 
there  are  a  few  substances  known  which,  like  sulphuric 
acid,  give  a  molecular  lowering  of  only  one-half  that  pro- 
duced by  the  non-electrolytes.  In  benzene  there  are 
also  a  few  exceptions,  but  in  this  case,  the  substances 
which  give  only  half  the  molecular  lowering  of  the 
normal,  are  either  non-electrolytes  like  the  alcohols,  or 
weakly  dissociated  acids  like  formic,  acetic,  benzoic,  etc. 
The  probable  significance  of  the  small  molecular  lowering 
produced  by  some  substances  is,  that  they  are  in  a  state  of 
molecular  aggregation  in  the  particular  solvent.  When 
the  molecular  lowering,  in  the  case  of  two  undissociated 
compounds  dissolved  in  a  given  solvent,  is  twice  as  great 
for  one  as  for  the  other,  it  means  that  twice  as  many  mole- 
cules of  the  second  are  aggregated  into  a  unit,  as  of  the 
first.  If  the  molecules  of  the  one  exist  singly  in  solution, 
those  of  the  second  are  combined  in  twos.  This  will  be 
seen  at  once,  if  we  remember  that  the  lowering  of  the 
freezing-point  of  a  solvent  depends  only  on  the  relative 
number  of  parts  of  the  solvent  and  of  the  dissolved  sub- 
stance. 

When  we  come  to  the  results  with  water  as  a  solvent, 
we  have  to  deal  with  an  entirely  new  set  of  phenomena. 
The  results  given  above  are  a  few  taken  from  a  large 
number.  Compounds  like  the  non- electrolytes,  give  a 
molecular  lowering  for  water,  which  is  very  nearly  a 
constant,  and  which  is  approximately  18.8.  This  is 
true  for  such  a  large  number1  of  substances  which  have 

*  Ann.  chim.  phys.  [5],  28,  137. 


THE   FREKZING-POINT   METHOD  5 

been  investigated  that  there  is  no  reason  for  regarding 
them  as  being  the  exceptions.  On  the  other  hand,  all 
the  strong  electrolytes,  including  the  strong  acids, 
strong  bases,  and  salts  of  strong  acids  with  strong  bases, 
weak  acids  with  strong  bases,  and  weak  bases  with 
strong  acids,  give  molecular  lowerings  which  are  greater 
than  the  value  18.8.  The  explanation  which  has  been 
offered  to  account  for  this  and  related  facts  by  Ar- 
rhenius,1  is  that  the  molecules  of  the  electrolytes  do  not 
exist  as  such  in  water  solution.  They  are  dissociated  into 
parts  called  ions,  and  the  amount  of  such  dissociation 
depends,  for  a  given  substance,  chiefly  upon  the  amount 
of  water  present — on  the  dilution  of  the  solution.  In  a 
very  dilute  solution  of  a  strongly  dissociated  electrolyte, 
we  have  practically  no  molecules  present,  only  ions.  If 
the  molecule  is  binary,  each  yields  two  ions,  and  since 
an  ion  lowers  the  freezing-point  as  much  as  a  molecule, 
the  molecular  lowering  for  such  substances,  at  high  dilu- 
tion, is  twice  as  great  as  where  there  is  no  dissociation. 
If  the  molecule  dissociates  into  three  ions,  and  the  dilu- 
tion is  such  that  the  dissociation  is  complete,  the  lower- 
ing of  the  freezing-point  will  be  three  times  as  great  as 
where  there  is  no  dissociation  as  with  the  non-electro- 
lytes. 

It  is  stated  above  that  in  aqueous  solutions  the 
molecules  break  down  into  parts  called  ions.  It  is  so 
easy  to  confuse  ions  with  atoms,  and  this  is  so  fre- 
quently done,  that  a  word  of  caution  here  is  hardly  out 
of  place.  An  ion  is  not  an  atom,  but  is  an  atom 
charged  with  electricity.  The  resemblance  between 
the  two  is  far  less  close  than  might  be  imagined,  except 
in  weight.  The  properties  of  many  of  the  atoms  could  not 
be  foretold  from  the  properties  of  the  ions,  with  any  de- 

1  Ztschr.  phys.  Chem.,  i,  631. 


6  THE   FREEZING-POINT   METHOD 

gree  of  probability.  An  atom  of  potassium  has  proper- 
ties so  different  from  an  ion  of  potassium,  that  one  is 
more  impressed  by  their  difference  than  by  their  re- 
semblance. 

In  some  cases,  as  with  the  non-electrolytes,  we  have 
then  to  deal  only  with  molecules  in  solutions  in  water, 
while  with  the  electrolytes  we  have  both  molecules  and 
ions,  or  only  ions,  depending  on  the  dilution  of  the  solu- 
tion. 

That  the  true  value  of  the  molecular  lowering  for 
water,  when  there  is  neither  molecular  aggregation  nor 
electrolytic  dissociation,  is  18.8,  has  been  shown  theo- 
retically by  van't  Hoff,1  and  more  clearly  presented  by 
Ostwald,2  thus  : 

Given  a  solution  which  contains  n  molecules  of  the 
dissolved  substance  and  N  molecules  of  the  solvent. 
L,et  T  be  the  temperature  of  solidification  of  the  solvent 
and  d  the  lowering  of  its  freezing-point.  I^et  enough  of 
the  solvent  solidify  to  dissolve  a  molecule  of  the  sub- 

f  N  \ 

stance,    (  —  molecules  ) .     L,et  A.  be  the  molecular  heat 
\  n  / 

of  fusion  of  the  solvent,  the  amount  of  heat  set  free  = 

N 
—A..     If  the  ice  is  now  separated  from  the  solution, 

warmed  to  the  temperature  Tt  fused,  and  finally  allowed 
to  mix  with  the  solution  which  has  also  been  warmed  to 
the  same  temperature,  by  passing  through  a  semi-per- 
meable membrane,  an  osmotic  pressure  p  will  be  ex- 
erted. If  the  volume  of  the  solvent  which  solidified  is 

N 
v,  the  work  equals  pv,  the  heat  — A., 


1  Ztschr.  phys.  Chem.,  i,  481. 

a  I^ehrbuch  allgem.  Chem.,  i,  760. 


THE   FREEZING-POINT   METHOD 


But/z;  =  XT  and  R=  2  cal.     Substituting  we  have  : 


n 

A  —  _  . 

'  N 


I,et  M  be  the  molecular  weight  of  the  solvent,  and 

A7      100          - 
placing  N=  —JT-J-  ,  we  have  : 

2T* 


100 


In  the  Raoult  formula  m  =  -j-t    m  is  the    molecular 

jrL 

weight  of  the  dissolved  substance,  A  is  the  specific  low- 

A 
ering  of  the  freezing-point,  which  equals  —  ,   in  which  p 

is  the  percentage  composition,/  of  the  solution,  and  C  is 
a   constant,     n,    the   number  of   molecules  of   the  dis- 

solved substance  in  100  grams  of  the  solvent  — 


m  =  - 


-          mA  =  Cmn. 


A  =  Cn 

From  (i)  and  (2)  we  have  : 
/-* 


(2) 


M    2T* 


100 


If  L  is  the  latent  heat  of  fusion  of  a  gram  of  the  sol- 
vent, A.  =  L,M,  and 

n  V2 

C  — 


ioo L' 

The  absolute  temperature  T,  for  the  freezing-point  of 
water,  is  273°,  and  L,  the  latent  heat  of  fusion  of  a  gram 
of  water,  was  taken  by  van't  Hoff  as  79°. l  When  these 

i  Ztschr.  phys.  Chem.,  i,  497. 


8  THE    FREEZING-POINT   METHOD 

values  are  inserted  in  the  above  expression,  C=  18.9. 
The  value  of  L  is  probably  more  nearly  79.7  when 
C  becomes  18.8. 

I  have  shown  experimentally1  that  the  value  of  C  for 
water,  as  determined  with  solutions  of  urea,  ethyl  and 
propyl  alcohols,  is  respectively  : 

18.88 
18.76 
18.77 

The  formula  of  van't  Hoff  applies  to  the  calculation 
of  the  constant  for  any  solvent. 

The  freezing-point  method  has  thus  two  distinct  ap- 
plications :  To  determine  the  molecular  weight  of  com- 
pounds in  solution,  which  are.  not  dissociated  by  the 
solvent  ;  and  to  measure  the  amount  of  the  dissociation  of 
electrolytes  in  solutions  of  different  concentrations. 

The  applicability  of  the  freezing-point  method  to  the 
determination  of  the  molecular  weights  of  substances  in 
solution,  was  pointed  out  by  Raoult.2  If  we  represent 
the  unknown  molecular  weight  of  a  substance  by  m,  the 
molecular  lowering  or  constant  for  the  solvent  by  C, 
and  the  lowering  of  one  per  cent,  of  the  dissolved  sub- 
stance by  S,  we  have 

C 


If  the  weight  of  the  solvent  used  is  W,  that  of  the  dis- 
solved substance  w,  and  the  observed  lowering  of  the 
freezing-point  -^, 

AW 
o  — 


100  W 


1  Ztschr.phys.  Chem.,  12,  653. 

2  Compt.  rend.,  101,  1056. 


THE    FREEZING-POINT   METHOD  9 

Substituting  this  value  of  5  in  the  above  expression,  it 
becomes 

loo  Cw 

—sw~- 

If  the  constant  C  is  multiplied  by  100  and  termed  C', 
the  expression  becomes 

Cw 

=^w- 

The  values  of  C1  for  a  number  of  the  solvents  most 
commonly  used  are 

c\ 

Water 1880 

Benzene 4900  6*t;£ 

Phenol 75oo 

Formic  acid 2770 

Acetic  acid 3880 

Nitrobenzene 7070 

The  Applicotion  of  the  Freezing-Point  Method  to  the  De- 
termination of  Molecular  Weights  in  Solution 

Beckmann1  has  devised  a  form  of  apparatus  which  is 
both  simple  and  efficient.  C  (Fig.  i)  is  a  small  glass 
battery- jar  covered  with  some  poorly  conducting  sub- 
stance, and  which  is  filled  with  the  freezing  material. 
A  mixture  of  finely  powdered  ice  and  salt  is  convenient. 
B  is  a  thick- walled  glass  tube,  into  which  tube  A,  con- 
taining the  solution,  is  inserted.  A  side  tube  attached 
to  tube  A,  is  thought  to  be  useful  in  introducing  the 
substance  whose  molecular  weight  is  to  be  ascertained, 
but  can  readily  be  dispensed  with.  The  thermometer, 
of  the  Beckmann  differential  type,  is  fitted  into  the  tube 
A,  by  means  of  a  cork,  which  can  be  easily  removed. 
The  stirrer  S  passes  through  the  same  cork,  and  must 

l  Ztschr.  phys.  Chem.,  2,  638. 


10 


THE   FREEZING-POINT   METHOD 


be  of  such  form  and  dimensions  as  to 
move  freely  up  and  down  between  the 
inner  walls  of  the  tube  and  the  bulb 
of  the  thermometer. 

A  small  glass  rod,  bent  at  the  bot- 
tom in  the  form  of  a  ring,  which  will 
easily  enter  the  glass  tube  A,  is  quite 
efficient.  A  short  piece  of  glass  tubing, 
through  which  this  rod  will  move 
freely,  is  forced  through  a  hole  in  the 
cork  at  the  top  of  tube  A,  and  serves 
both  to  hold  the  stirrer  in  place,  and  to 
allow  smoother  movement  through  the 
cork.  The  apparatus  of  the  follow- 
ing dimensions  has  been  found  in  this 
laboratory  to  be  convenient. 

Tube  A  is  20  cm.  in  length  and  3 
cm.  in  width.  B  is  about  15  cm.  long 
and  5  cm.  wide.  The  glass  tube  used 
in  constructing  the  stirrer  should  be 
about  2.5  mm.  in  thickness.  A  ther- 
mometer with  a  short,  thick  bulb, 
such  as  is  sometimes  furnished  on  the 


Fig.  i. 

market,  is  not  as  desirable  as  one  whose  bulb  is  longer 
and  of  smaller  diameter,  since  it  requires  a  longer  time 
to  register  the  temperature  of  the  liquid. 

In  case  the  solvent  used  is  hydroscopic,  some  precau- 
tion must  be  taken  to  protect  it  from  the  moisture  in  the 
air.  An  apparatus,  satisfying  this  requirement,  has 
been  constructed  also  by  Beckmann,1  by  forcing  the  air 
which  enters  the  apparatus  to  pass  over  some  drying 
agent,  like  sulphuric  acid.  The  device  is  shown  in 

1  Ztschr.  phys.  Chem.,  7,  324. 


THK   FREEZING-POINT  METHOD 


II 


Fig.  2.      The  handle  of  the  stirrer  E  passes  through  a 
glass  tube,  into  which  the 
side  tube  F,  containing  a 
few  drops  of  sulphuric  acid, 
is  fused.      The  air  enters 
through  this  side  tube,  is 
dried,   and   passes  out 
through  the  tube  receiving 
the  handle  of  the  stirrer. 
The  remainder  of  the  appa-  ''Ss^ 
ratus  is  of  exactly  the  same        "Ck 
form  as   shown  in  Fig.  i,  |j 

except  that  it  is  provided  H 
with  a  glass  siphon  H,  for 
removing  the  melted  freez- 
ing-mixture. This  is  really 
superfluous,  since  a  piece 
of  rubber  tubing  answers 
the  purpose  equally  well. 

Forms   of  apparatus  far 
more   accurate  than  those  Fig.  2. 

just  described,  have  been  devised  and  used,  but  since  such 
extra  refinement  is  desirable  rather  to  measure  dissocia- 
tion than  to  determine  molecular  weights,  reference  will 
be  given  to  them  under  the  second  application  of  the 
freezing-point  method. 

Carrying:  Out  a  Determination 

The  thermometer  must  first  be  so  adjusted  that  the 
freezing-point  of  water  falls  near  the  top  of  the  scale. 
To  accomplish  this,  water  is  poured  into  the  tube  A, 
until  the  bulb  of  the  thermometer,  when  placed  in  posi- 
tion, is  covered.  Tube  A  is  placed  directly  in  the  freez- 
ing-mixture in  C,  and  the  water  allowed  to  freeze.  As 


12  THE   FREEZING-POINT   METHOD 

soon  as  fine  particles  of  ice  separate,  tube  A  is  removed 
from  the  freezing-mixture,  placed  in  tube  B,  and  the 
whole  then  placed  again  in  the  freezing-mixture.  The 
thermometer  is  then  raised  out  of  the  water  containing 
ice  particles,  allowed  to  remain  in  contact  with  the 
warmer  air  a  moment,  and  then  given  a  sudden  jar. 
The  mercury  falls  from  the  top  to  the  bottom  of  the  up- 
per cup,  and  leaves  the  column  free  at  its  upper  end. 
The  thermometer  is  then  placed  again  in  the  ice-cold 
water,  and  if  the  end  of  the  mercury  column  does  not 
come  to  rest  on  the  upper  half  of  the  scale,  the  process 
just  described  is  repeated.  A  few  trials  generally  suffice 
to  bring  the  reading  approximately  where  desired. 

The  thermometer  being  adjusted,  tube  A  is  carefully 
dried,  closed  at  the  top  and  side  with  wooden  stoppers, 
and  weighed.  Knough  pure  water  is  poured  into  the  tube 
to  cover  the  bulb  of  the  thermometer  when  in  position, 
and  the  tube  is  again  weighed.  The  weight  of  the  sol- 
vent employed  is  thus  determined.  The  stopper  is  then 
removed  from  the  top  of  the  tube  and  the  thermometer 
and  stirrer  placed  in  position.  Tube  A  is  placed  in  tube 
B,  and  the  whole  system  in  the  freezing-mixture.  Dur- 
ing the  cooling  of  the  solvent  the  stirrer  should  be  raised 
and  lowered  frequently.  The  water  will  cool  down  be- 
low its  freezing-temperature  often  a  degree  or  more,  before 
the  ice  will  begin  to  separate.  When  the  undercooling 
of  the  solvent  or  of  a  solution  is  very  much  more  than 
a  degree,  a  small  fragment  of  pure  ice  should  be  thrown 
into  the  overcooled  liquid.  This  will  start  the  separa- 
tion of  ice,  which  will  continue  until  the  true  freezing- 
temperature  is  reached. 

When  the  ice  begins  to  separate,  the  mercury  column 
will  rise,  rapidly  at  first,  then  slower,  until  it  reaches 
the  point  of  equilibrium.  While  the  thermometer  is 


THE   FREEZING-POINT   METHOD  13 

rising,  and  especially  when  near  the  point  of  rest,  it 
must  be  tapped  gently  to  prevent  the  mercury  from  lag- 
ging back  in  the  capillary,  due  to  friction  against  its 
walls.  A  lead  pencil  is  convenient  to  use  in  jarring  the 
thermometer.  The  freezing-point  of  the  water  is  then 
noted  on  the  thermometer.  The  reading  on  the  ordi- 
nary Beckmann  instrument  can  easily  be  made  to  0.001° 
by  means  of  a  small  pocket  lens. 

The  tube  containing  the  solvent,  with  the  thermome- 
ter and  stirrer  in  position,  is  removed  from  the  freezing- 
mixture,  and  the  ice  melted,  by  seizing  the  tube  for  a 
few  moments  with  the  hand.  The  freezing-point  of  the 
water  is  then  redetermined  exactly  as  described  above. 
The  two  determinations  should  not  differ  more  than  two- 
or  three-thousandths  of  a  degree. 

The  substance  whose  molecular  weight  is  to  be  deter- 
mined, is  weighed  in  a  weighing  tube,  poured  into  the 
solvent,  and  brought  completely  into  solution.  If  cane- 
sugar  is  used,  that  quantity  is  taken  which  will  give  a 
solution  about  one-tenth  normal.  If  urea,  or  any  of  the 
alcohols  is  used,  a  more  concentrated  solution  may  be 
employed.  A  solution  of  cane-sugar,  dextrose,  etc.,  more 
concentrated  than  one-tenth  normal,  gives  abnormally 
large  depressions  of  the  freezing-point  of  water.  The 
reason  for  this  is  not  entirely  clear.  The  solution  is  then 
placed  in  the  freezing-mixture  and  its  freezing-point  de- 
termined, and  redetermined,  exactly  as  described  for  the 
solvent.  All  the  data  are  thus  available  for  calculating 
the  molecular  weight  of  the  substance  from  the  expres- 
sion already  given. 

Correction  for  the  Separation  of  Ice 

A  certain  amount  of  the  solvent  separates  in  the  solid 
form  in  all  such  determinations,  and  the  solution  be- 


14  THE    FREEZING-POINT   METHOD 

comes  concentrated  by  just  this  amount.  The  freezing- 
point  of  the  solution,  as  read  on  the  thermometer,  is  there- 
fore always  lower  than  would  correspond  to  a  solution  of 
the  concentration  originally  used.  A  correction  for  the 
change  in  concentration,  due  to  the  separation  of  the 
solid  solvent,  must  be  introduced.  The  amount  of  the 
solvent  which  separates  in  the  solid  phase,  can  easily  be 
determined,  knowing  the  amount  by  which  the  solution 
is  undercooled  before  the  ice  begins  to  separate,  the  la- 
tent heat  of  fusion  of  a  unit  quantity  of  the  solvent,  and 
the  specific  heat  of  the  liquid.  The  fraction  of  the  sol- 
vent which  separates  is  calculated  thus,  as  was  pointed 
out  by  the  present  writer  :l 

If  we  represent  by  u  the  amount  of  the  undercooling 
of  the  solution  in  degrees  centigrade,  by  w  the  latent 
heat  of  fusion  of  unit  weight  of  the  solvent,  by  s  the  spe- 
cific heat  of  the  liquid,  and  by  T the  fraction  which  will 
solidify,  we  have 

r=i, 

w 

When  water  is  used  as  a  solvent  j=  i,  and  a/ =80. 
The  fraction  of  this  solvent  which  will  separate  as  a  solid, 
for  every  degree  of  undercooling,  is  therefore  -g^,  and 
the  concentration  of  the  original  solution  is  increased  by 
just  so  much.  Instead  of  applying  the  correction  to  the 
concentration,  it  is  simpler  to  apply  it  directly  to  the 
freezing-point  lowering  itself. 

The  Application  of  the   Freezing-Point   Method  to  the 
Measurement  of  Electrolytic  Dissociation 

An  ion  lowers  the  freezing-point  of  a  solvent  just  as 
much  as  a  molecule.  If  a  molecule  dissociates  into  two 
ions  it  will  lower  the  freezing-point  of  a  given  amount  of 

1  Ztschr.  phys.  Chetn.,  12,  624. 


THE   FREEZING-POINT   METHOD  15 

a  solvent,  just  twice  as  much  as  if  it  is  not  dissociated. 
The  lowering  of  the  freezing-point  of  a  given  sol- 
vent by  a  partially  dissociated  electrolyte,  depends  upon 
the  relation  between  the  number  of  molecules  of  the  sol- 
vent, and  the  sum  of  the  molecules  plus  the  ions  of  the 
dissolved  substance.  Thus,  it  is  possible  for  any  given 
dilution,  to  determine  the  amount  to  which  an  electro- 
lyte is  dissociated.  The  calculation  of  the  dissociation 
from  the  freezing-point  lowering  is  simple.  The  molecu- 
lar lowering  of  the  freezing-point  of  any  solvent  by  any 
substance  was  defined  by  Arrhenius1  as  the  lowering 
produced  by  a  gram-molecular  weight  of  the  substance 
in  a  liter  of  solution.  This  can  be  taken  as  approxi- 
mately one-tenth  of  the  molecular  lowering  as  defined 
by  Raoult.  For  our  present  purpose  we  accept  the 
definition  of  Arrhenius,  and  find  that  the  molecular  low- 
ering of  water  produced  by  a  gram-molecular  weight  of 
a  non-electrolyte,  like  urea,  the  alcohols,  etc.,  in  a  liter 
of  solution,  is  the  constant  1.88°.  If  the  substance 
used  is  dissociated,  the  molecular  lowering  is  always 
greater  than  1.88°.  The  first  step  is  to  calculate  the 
molecular  lowering  for  the  solution  in  question,  which 
is  done  by  dividing  the  lowering  found,  by  the  concen- 
tration in  decimal  part  of  normal.  If  there  were  only 
molecules  present  the  molecular  lowering  would  be  1.88°. 
The  molecular  lowering  found  must  therefore  be  divided 
by  1.88,  which  gives  the  value  of  the  van't  Hoff  coeffi- 
cient 2,  for  the  solution.8 

Molecular  lowering . 

1.88 

If  the  molecule  breaks  down  into  two  ions,  the  percent- 

1  Ztschr.  phys.  Chem.,  a,  494. 
,501. 


1 6  THE   FREEZING-POINT   METHOD 

age  of  dissociation,  tf1  (Arrhenius  activity  coefficient),  is 
expressed  thus 

a  =  /  —  i . 
If  the  molecule  breaks  down  into  three  ions, 

i —  i 

a  = 

If  into  n  ions, 


n —  i 

The  Method  of  Work 

Exactly  the  same  apparatus  may  be  used  as  was  em- 
ployed in  the  determination  of  molecular  weights.  The 
method  of  preparing  the  solutions  is,  however,  some- 
what different. 

The  solvent  is  poured  into  the  innermost  vessel  in 
quantity  large  enough  to  cover  the  bulb  of  the  thermom- 
eter, and  its  freezing-point  upon  the  thermometer  ascer- 
tained, as  in  a  molecular  weight  determination.  The 
solvent  is  then  completely  removed  from  the  vessel  and 
the  solution  of  known  concentration,  prepared  in  a  measur- 
ing flask,  introduced.  Its  freezing-point  is  then  deter- 
mined exactly  as  previously  described,  including  the  rapid 
stirring,  the  tapping  of  the  thermometer,  the  introduc- 
tion of  a  fragment  of  the  solid  solvent  when  necessary, 
and  the  correction  for  the  change  in  concentration  due 
to  the  separation  of  the  solid  solvent.  The  dilution  of 
the  solution  is  then  increased  one  and  a  half,  two,  three, 
four  times,  etc.,  and  the  dissociation  determined  for  each 
dilution.  It  will  be  found  that  the  value  of  i,  and  there- 
fore of  of,  always  increases  with  increase  in  dilution.  In 

1  Ztschr.  phys.  Chem.,  n,  535. 


THE   FREEZING-POINT   METHOD  17 

this  work  any  of  the  common  chlorides,  nitrates,  bro- 
mides, or  in  general  any  electrolyte  may  be  used. 

It  is  convenient  to  use  a  solution  of  pure  sodium  or 
potassium  chloride  of  concentration  about  0.5  normal, 
and  then  to  increase  the  dilution  of  this  solution  in 
several  steps,  as  indicated  above.  The  chlorides  and 
nitrates  break  down  into  two  ions  each,  the  sulphates 
into  three.  The  values  of  a  from  the  freezing-point 
method  should  be  preserved  and  compared  with  the  values 
of  OL  for  the  same  solutions,  as  obtained  by  the  conduc- 
tivity method. 

Far  more  accurate  experimental  methods  have  been 
devised  and  used  for  measuring  the  freezing-point  lower- 
ings,  by  Loomis,1  Nernst  and  Abegg,2  Ponsot,3  myself,4 
and  others. 

A  form  of  apparatus,  which  was  found  by  the  writer 
to  give  excellent  results,  is  sketched  in  Fig.  3. 

A  is  a  large  metallic  vessel,  25  cm.  high  and  35  cm. 
wide.  This  is  surrounded  by  a  mantle  of  non-conducting 
material  to  protect  it  from  the  warmer  air.  B  is  a  ves- 
sel of  zinc,  21  cm.  high  and  15  cm.  wide,  which  rests  upon 
a  tripod,  to  diminish  the  surface  of  contact  with  the  outer 
vessel.  This  is  provided  with  a  lid  of  zinc.  The  vessel 
B  is  completely  surrounded,  except  above,  with  a  freez- 
ing-mixture of  ice  and  a  little  salt.  The  space  be- 
tween A  and  B,  filled  with  the  freezing-mixture,  was 
covered  with  the  ring  of  asbestos,  aa,  to  protect  the 
freezing-mixture  from  the  air.  C  is  a  glass  vessel,  18 
cm.  high,  10  cm.  wide,  and  of  about  1200  cc.  capacity. 
This  rests  on  a  thick  felt  bottom,  which  protects  it  from 
the  zinc  vessel  beneath.  The  space  between  B  and  C  is 

1  Ber.  d.  chem.  Ges.,  26,  797 ;  Wied.  Annalen,  51,  500. 

2  Ztschr.  phys.  Chem.,  15,  681. 
«  Compt.  rend.,  122,  668. 

*  Ztschr.  phys.  Chem.,  n,  no,  529. 


i8 


THE   FREEZING-POINT   METHOD 


filled  with  air  and  covered  above  with  a  ring  of  felt, 
bb,  which  rests  on  a  metallic  shelf  fastened  on  to  the 
inner  side  of  the  vessel  B.  The  air-chamber  between 
B  and  C  is  thus  closed  and  remains  at  nearly  the  same 
temperature  during  a  determination.  The  glass  ves- 
sel was  covered  with  a  glass  lid.  D  is  a  thermometer 


whose  bulb  is  14  cm.  in  length  and  1.5  cm.  in  width.  The 
fine  capillary  was  carefully  calibrated.  The  entire  scale, 
which  was  22  cm.  in  length,  corresponded  to  only  0.6°.  It 
was  divided  into  tenths,  hundredths,  and  thousandths  of 
a  degree.  The  finest  divisions  could  be  estimated  to 
tenths,  through  a  telescope,  so  that  the  scale  could  be 


THE    FREEZING-POINT   METHOD 


read  to  o.oooi  of  a  degree.  The  thermometer  was  of 
the  Beckrnann  type,  and  the  freezing-point  of  the  sol- 
vent could  be  adjusted  upon  the  scale,  wherever  desired. 
It  was  fastened  firmly  in  cork  c,  and  passed  loosely 
through  g,  being  suspended  in  the  liquid  in  C. 

E  is  a  stirrer,  which  was  constructed  as  follows  :  A 
circular  piece  of  sheet-silver  was  cut  somewhat  smaller 
than  the  glass  vessel,  and  plated  electrolytically  with 
gold.  This  was  cut  along  the  circular  lines  shown  in 
Fig.  4,  and  also  horizontally,  as  shown.  The  ends 


marked  o  were  bent  upwards,  those  marked  u  down- 
wards. S  is  a  small  hole  which  received  the  handle.  P 
is  a  large  hole  in  the  center,  through  which  the  bulb  of 
the  thermometer  passed.  In  Fig.  5  is  given  a  section 


/ 


across  one  of  the  openings,  to  show  how  the  ends  are 
cut  and  bent.  This  section  corresponds  to  the  dotted 
line  a,b  in  Fig.  4. 

A  stirrer  of  this  form  has  the  advantage  that  at  every 


20  THE    FREEZING-POINT   METHOD 

movement  up  and  down  the  liquid  is  moved  horizontally 
and  vertically,  and  any  currents  set  up  during  the  stroke 
in  one  direction  are  completely  reversed  by  the  opposite 
stroke.  The  advantage  claimed  for  this  method  is  that 
by  using  a  large  volume  of  the  solution  the  temperature 
can  be  much  better  regulated.  The  comparatively  thick 
layer  of  air  at  constant  temperature,  around  the  inner- 
most vessel,  makes  it  far  less  susceptible  to  the  influ- 
ence of  changes  in  the  temperature  of  surrounding  ob- 
jects. The  large  volume  of  the  liquid  exposes  rela- 
tively less  surface  to  the  cooling  mixture,  and  the  rate  of 
cooling  is  comparatively  slow.  This  makes  it  possible 
to  determine  more  accurately  the  temperature  of  the 
liquid  in  which  the  ice  separates.  Since  the  rate  of 
cooling  is  slow,  the  ice  which  separates  during  the  time 
required  for  the  thermometer  to  become  constant,  is 
relatively  small. 

A  liter  of  pure  water  is  placed  in  the  vessel  C,  and  its 
freezing-point  determined  on  the  thermometer.  A  cer- 
tain volume  of  this  is  then  removed,  and  an  equal  vol- 
ume of  a  solution  of  known  concentration,  added.  Thus 
the  volume  of  the  solution  in  the  vessel  always  remains 
a  liter,  which  facilitates  the  calculation  of  the  results. 
The  same  process  is  repeated  in  making  successive  di- 
lutions. By  this  method  of  work  the  first  solution  of  a 
series  is  the  most  dilute,  and  these  become  more  and 
more  concentrated  to  the  end  of  the  series. 

Such  accuracy  as  is  reached  with  this  apparatus  is  not 
absolutely  necessary  for  laboratory  practice,  but  is  very 
desirable  where  the  problem  of  the  measurement  of  elec- 
trolytic dissociation  presents  itself. 

The  applicability  of  the  method  will  be  seen  by  com- 
paring the  values  of  the  dissociation  of  a  number  of 


THE    FREEZING-POINT   METHOD 


21 


acids,  bases,  and  salts,  as  obtained  by  it,1  with  the  dis- 
sociation as  determined  by  the  conductivity  method  of 
Kohlrausch.2 


Concentration 
Substance.          normal. 


Dissociation 

from 

conductivity. 
Per  cent. 


Dissociation  from 

lowering  of 

freezing-point. 

Per  cent. 


NaCl o.ooi  98.0  98.4 

o.oio  93.5  90.7 

o.ioo  84.1  83.5 

K2SO4 0.002  92.2  94.1 

o.oio  85.8  88.2 

o.ioo  70.1  72.0 

BaCl2 0.002  93.9  94.1 

o.oio  87.9  88.4 

o.ioo  75.3  76.8 

HC1 0.002  100. o  98.4 

o.oio  98.9  95.8 

o.ioo  93.9  88.6 

H2SO4 0.003  89.8  86.0 

0.005  85.4  83.8 

0.050  62.3  60.7 

HNO3 0.002  loo.o  98.4 

o.oio  98.5  96.8 

o.ioo  93.5  87.8 

H3PO4 0.002  87.8  85.2 

o.oio  63.5  68.8 

KOH 0.002  100.0  98.4 

o.oio  99.2  93.7 

o.ioo  92.8  83.1 

NaOH 0.002  98.9  98.4 

o.oio  99.5  93.7 

0.050  90.4  88.4 

An    absolute    agreement    between    the    dissociation 
values  obtained  by  the  conductivity  method  and  by  the 

l  Ztschr.  phys.  Chem.,  12,  639, 
«  Wied.  Annalen,  26,  161. 


22  THE   FREEZING-POINT   METHOD 

freezing-point  method,  is  not  to  be  expected,  since  the 
former  method  was  used  at  18°  or  25°,  while  the  latter  was 
applied  at.  about  o°. 


PART  II 


THE  BOILING-POINT  METHOD 


Theoretical 

The  presence  of  a  foreign  non-volatile  substance 
diminishes  the  vapor  pressure  of  the  solvent  in  which  it 
is  dissolved.  Since  the  boiling-point  of  a  solvent,  or  of 
a  solution,  is  the  temperature  at  which  the  vapor-pres- 
sure just  overcomes  the  pressure  of  the  atmosphere,  it 
follows  that  the  solution  having  a  lower  vapor-pressure 
than  the  solvent,  will  have  a  higher  boiling-point. 

There  are  thus  two  quantities,  either  of  which  we  may 
measure  :  the  depression  of  the  vapor-tension  of  the  sol- 
vent, caused  by  the  presence  of  the  dissolved  substance ; 
or  the  rise  in  the  boiling-point  of  the  solvent,  due  to  the 
same  cause. 

Passing  over  the  work  of  Faraday,1  Griffiths,2  Legrand,3 
and  others,  along  this  line,  since  it  all  fell  short  of  any 
very  important  generalization,  we  come  to  that  of  von 
Babo,4  who  found  that  the  relation  between  the  amount 
of  salt  present  and  the  diminution  of  the  vapor-pressure, 
was  independent  of  the  temperature. 

The  work  of  Wiillner5  was  of  greater  significance.  He 
measured  the  depression  of  the  vapor-pressure  of  water 
especially  by  salts,  and  arrived  at  the  conclusion  that 
the  diminution  of  the  vapor-pressure  of  water,  pro- 

1  Ann.  chim.  phys.,  ao,  324. 

2  Pogg.  Annalen.  2,  227. 

*  Ann.  chim.  phys.,  5p,  423. 

*  Jahrb.  Chem.,  1848-49,  93  ;  1857,  72. 
5  Pogg.  Anualen,  103,  529  ;  io5,  85. 


24  THE   BOILING-POINT   METHOD 

duced  by  dissolved  non- volatile  substances,  was  pro- 
portional to  the  amount  of  substance  present. 

While  this  is  true  only  in  certain  cases,  or  indeed  only 
for  certain  classes  of  compounds,  yet  it  is  strictly  analo- 
gous to  the  earliest  generalization  reached  in  connection 
with  the  study  of  the  depression  of  the  freezing-point  of 
a  solvent  by  a  foreign  substance.  It  will  be  remembered 
that  Blagden  stated  that  the  depression  of  the  freezing- 
point  of  a  solvent  by  a  dissolved  substance  was  propor- 
tional to  the  amount  of  substance  present. 

When  depressions  of  the  freezing-point  were  measured 
with  a  fair  degree  of  accuracy,  it  was  shown  that  the 
generalization  of  Blagden  held  only  approximately,  and 
in  some  cases.  So  also,  the  relation  pointed  out  by 
Wiillner  was  shown  to  be  only  an  approximation  under 
certain  conditions,  by  the  work  of  Pauchon,1  Tammann8 
and  Kmden.3 

It  is  to  Raoult,  more  than  to  any  other,  that  we  owe 
the  theoretical  development  of  the  subject  in  hand. 

He  employed  the  first  of  the  two  quantities  men- 
tioned, and  measured  the  depression  of  the  vapor- tension 
of  a  solvent  by  foreign  substances.  A  number  of  rela- 
tions were  brought  out  by  him  from  a  study  of  solutions 
in  solvents  other  than  water,  which  would  not  have  been 
discovered  in  aqueous  solutions,  since  these  are  often  dis- 
sociated, and  to  a  different  amount  for  different  dilutions. 

Raoult4  confirmed  the  generalization  of  von  Babo, 
that  the  relation  between  the  depression  of  the  vapor- 
pressure  and  the  vapor-pressure  of  the  solvent,  was  in- 
dependent of  the  temperature  between  o°  and  20°.  Also 
that  of  Wiillner,  that  the  depression  of  the  vapor-pres- 

1  Compt.  rend.,  89,  752. 

2  Wied.  Annalen,  24,  523. 
8  Ibid,  31,  145. 

*  Compt.  rend.,  103,  1125. 


THE    BOIIvING-POINT   METHOD  25 

sure  was  proportional  to  the  concentration  (when  there 
was  no  dissociation) . 

If  we  represent  the  vapor-pressure  of  the  pure  solvent 
by  /,  and  that  of  the  solution  by  p\ 

P-P' 

P 

is  independent  of  the  temperature  and  proportional  to 
the  concentration. 

The  nature  of  the  substance  used  was  then  investi- 
gated to  determine  whether  the  chemical  composition  of 
the  molecule  had  any  effect  on  its  power  to  depress  the 
vapor-tension. 

Solutions  containing  the  same  number  of  molecules  of 
different  substances  in  solution  in  the  same  number  of 
molecules  of  a  given  solvent,  must  be  compared  as  to 
their  vapor-pressures.  This  would  be  difficult  to  carry 
out  directly.  Convenient  concentrations  of  different 
substances  were  used,  the  vapor-pressures  of  the  solu- 
tions determined,  and  the  molecular  depression  of  the 
vapor-pressure  calculated  for  each  substance  from  the 
expression 

p—p'm 

~TXT' 

in  which  m  is  the  molecular  weight  of  the  substance, 
and  g  the  number  of  grams  in  100  grams  of  the  solvent. 

He  found  that  the  molecular  depression  of  the  vapor- 
pressure  of  a  solvent  is  a  constant  for  a  given  solvent, 
independent  of  the  nature  of  the  substance  which  is  dis- 
solved in  it.  This  holds,  as  we  now  know,  only  when 
the  dissolved  substances  are  undissociatgcTby  the  solvent. 

Raoult1  investigated  also  the  relative  diminution  of 
the  vapor-pressure  of  different  solvents,  when  the  rela- 

1  Compt.  rend.,  104,  1430. 


26  THE   BOILING-POINT   METHOD 

tion  between  the  number  of  molecules  of  the  substance 
and  that  of  the  solvent  was  the  same. 

Below  are  given  the  results  of  the  relative  diminution 
of  the  vapor-pressure  for  twelve  solvents,  calculated  on 
the  basis  of  one  molecule  of  the  substance  to  100  mole- 
cules of  the  solvent  : 

Water  .....................................  0.0102 

Phosphorus  trichloride  ....................  0.0108 

Carbon  bisulphide  .........................  0.0105 

Tetrachlormethane  ........................  0.0105 

Chloroform  ................................  0.0109 

Amylene  ..................................  0.0106 

Benzene  ...................................  0.0106 

Methyl  iodide  .............................  0.0105 

Methyl  bromide  ...........................  0.0109 

Ether  .....................................  0.0096 

Acetone  •  •  •  ................................  o.oioi 

Methyl  alcohol  ............................  0.0103 

The  relative  diminution  of  the  vapor-pressure  of  sol- 
vents produced  by  a^  molecule  of  a  non-  volatile  sub- 
stance, in  the  same  number  of  molecules  of  the  sol- 
vents, is  very  nearly  a  constant.  This  relation  has  been 
satisfactorily  formulated  thus  : 

p—p'_  n 

p  CN+n> 

in  which  n  is  the  number  of  molecules  of  the  dissolved 
substance,  N  that  of  the  solvent,  and  c  a  constant, 
which,  from  the  foregoing  table,  can  be  regarded  as 
unity.  The  expression  becomes  then 

p  —  p'  _         n 


or  the  lowering  of  the  vapor-pressure  of  the  solvent  is 
to  the  vapor-pressure  of  the  solvent,  as  the  number  of 
molecules  of  the  dissolved  substance  is  to  the  entire 


THE   BOILING-POINT   METHOD  27 

number  of  molecules  present.  This  expression  was 
tested  experimentally  by  Raoult,1  and  found  to  hold  for 
a  large  number  of  substances  in  ethereal  solution. 

From  the  foregoing  it  will  be  seen  that  the  molecular 
weight  of  substances  can  be  determined  directly  from  the 
depression  of  the  vapor-pressure  of  a  solvent  which  they 
produce. 

L,et  the  molecular  weight  of  the  substance  be  repre- 
sented by  m,  and  the  amount  used  by  a,  then  the  num- 

ber of  molecules,  n  =  —  . 
m 

Making  N=  i,  and  substituting  this  value  of  n  in 
the  expression 

P—P'=        "  & 

p  N+  n1 

we  have 


fa 

m=¥^~y 

Knowing/,  p'  and  a,  we  calculate  m  directly. 

As  a  practical  method  for  determining  molecular 
weights,  this  is  not  used,  since  such  measurements  are 
not  easily  carried  out,  and  are  not  very  accurate. 

It  has  been  found  to  be  simpler  and  more  accurate  to 
determine  the  temperature  at  which  the  vapor-pressure 
of  the  solution  is  equal  to  that  of  the  solvent.  Since  the 
boiling-point  of  a  liquid  is  the  temperature  at  which  its 
vapor-pressure  just  overcomes  the  pressure  of  the  atmos- 
phere, the  boiling-points  of  a  solvent  and  of  a  solution  in 
that  solvent,  are  the  temperatures  of  equal  vapor-pres- 
sures. The  object  is  then  to  determine  the  rise  in  the 

1  Ztschr.  phys.  Chem.,  2,  371. 


28  THE   BOILING-POINT   METHOD 

boiling-point  of  a  solvent  produced  by  the  substance  dis- 
solved in  it. 

The  experimental  method  for  carrying  out  such  de- 
terminations we  owe  to  Beckmann.  The  forms  of  appara- 
tus which  seem  best  adapted  to  this  work,  and  the  details 
of  an  experiment  will  be  considered  in  the  second  part 
of  this  chapter. 

The  rise  in  the  boiling-point  is  directly  proportional 
to  the  lowering  of  the  vapor-pressure,  and  depends  upon 
the  relative  number  of  molecules  of  the  solvent  and  of  the 
dissolved  substance. 

The  probability  of  calculating  molecular  weights 
directly  from  the  rise  in  the  boiling-point  of  solvents 
produced  by  substances  dissolved  in  them,  is  at  once  ap- 
parent. 

The  expression  by  which  the  molecular  weights  are 
calculated,  is  analogous  to  that  already  given  for  calcu- 
lating molecular  weights  from  lowerings  of  the  freezing- 
point  of  solvents  by  dissolved  substances.  If  we  repre- 
sent the  unknown  molecular  weight  by  m,  the  weight  of 
the  substance  used  by  wt  the  weight  of  the  solvent  by 
W,  and  the  rise  in  the  boiling-point  of  the  solvent  by  R, 
we  have 

Cw 

m  •=. 


in  which  C  is  a  constant  of  different  value  for  each  sol- 
vent. 

The  analogy  between  the  lowering  of  the  freezing- 
point  and  the  rise  in  the  boiling-point  holds  still  further, 
in  that  the  value  of  C  can  be  calculated  from  the  same 
formula  : 

c=-ill 

ioo  L 


THE    BOILING-POINT   METHOD  29 

When  applied  to  calculating  the  constant  for  the  boil- 
ing-point method  of  determining  molecular  weights,  T 
is  the  absolute  temperature  at  which  the  pure  solvent 
boils,  and  L  the  latent  heat  of  evaporation  of  the  solvent. 

The  values  of  C  for  a  number  of  the  solvents  more 
commonly  used,  are  given  below.  The  solvents  are 
arranged  in  the  order  of  their  boiling-points. 

JC.  Boiling-point. 

Ethyl  ether -ino  34.9 

Carbon  bisulphide 2370  46.0 

Acetone 1670  56.3 

Chloroform 3.660  60.2 

Ethyl  alcohol 1 150  78.3 

Benzene 2770          9  79.6 

Water   520  100.0 

Acetic  acid 2530  118.0 

Ethylene  bromide 6320  128.8 

Aniline 3220  184.5 

Some  of  the  relations  between  the  boiling-point  and 
the  freezing-point  methods  have  been  mentioned,  but 
others,  however,  exist.  It  will  be  remembered  that  the 
freezing-point  method  can  be  used  to  determine  the 
molecular  weights  of  only  a  limited  number  of  sub- 
stances— the  non-electrolytes.  The  boiling-point  method 
is  subject  to  the  same  limitation.  Those  substances 
which  give  abnormally  great  depressions  of  the  freezing- 
point,  due  to  electrolytic  dissociation,  give  abnormally 
great  depressions  of  the  vapor- tension,  or  rise  in  the 
boiling-point.  It  was  pointed  out  that  in  such  cases  the 
freezing-point  method  could  be  used  to  measure  the 
amount  of  the  dissociation  in  the  solutions.  The  boil- 
ing-point method  may  be  used  for  the  same  purpose,  but 
is  not  capable  of  the  same  degree  of  accuracy  as  the 
former. 


3O  THE   BOILING-POINT   METHOD 

Some  recent  work1  has  shown,  however,  that  it  can 
be  applied  to  the  problem  of  electrolytic  dissociation  in 
solution,  and  when  all  the  precautions  specified  are 
taken,  it  is  capable  of  giving  fairly  satisfactory  results. 

The  Application  of  the  Boiling-Point  Method  to  the  De- 
termination of  Molecular  "Weights  in  Solution 

The  precautions  which  are  necessary  in  making  such 
measurements  will  be  understood  best  by  pointing  out 
the  more  prominent  errors  to  which  the  boiling-point 
method  is  subject. 

The  method  as  such,  is  not  capable  of  that  refine- 
ment to  which  the  freezing-point  method  has  been  de- 
veloped. It  is  sensitive  to  barometric  changes,  which 
seriously  affect  the  boiling-point  of  liquids.  In  this 
method  the  vapor  escapes  quickly  from  the  solution 
in  which  its  presence  is  necessary  to  establish  the  tem- 
perature equilibrium.  The  difference  in  temperature 
between  the  liquid  and  surrounding  objects  is  generally 
much  greater  in  this  method  than  in  the  freezing-point 
method,  so  that  more  precautions  are  necessary  to 
protect  the  solution  and  thermometer  from  changes  in 
the  temperature  of  external  objects.  In  this  method  a 
part  of  the  comparatively  pure  solvent  is  constantly 
separating  from  the  solution  as  vapor,  and  is  returned 
as  a  liquid,  at  a  temperature  lower  than  that  of  the  boil- 
ing solution.  The  amount  of  this  liquid  cannot,  for 
given  conditions,  be  determined  with  the  same  degree  of 
accuracy  as  was  possible  in  ascertaining  the  amount  of 
ice  which  separated  in  the  freezing  liquid.  The  large 
Beckmann  thermometers  are  more  liable  to  undergo 
change  at  the  comparatively  high  temperatures  to 
which  they  are  subjected  in  this  method,  than  in  the 

i  Jones  and  King :  Am.  Chem.  J.,  19,  581. 


THE;   BOILING-POINT   METHOD  31 

freezing-method,  where  the  temperature  of  the  thermom- 
eter is  at  no  time  widely  removed  from  the  ordi- 
nary. The  boiling-point  method  has  this  advantage 
that  more  solvents  can  be  employed,  since  compara- 
tively few  solvents  freeze  within  the  range  of  ordinary 
temperatures  ;  and  further,  the  solubility  of  substances 
is  generally  increased  at  the  higher  temperatures.  It  is, 
on  the  other  hand,  a  misfortune  for  the  boiling-point 
method  that  aqueous  solutions  cannot  be  used  satisfac- 
torily, partly  because  of  the  very  small  constant  for 
water. 

A  number  of  forms  of  apparatus  for  determining  the 
boiling-point  of  solvents  and  solutions  have  been  de- 
vised by  Beckmann,1  to  whom  we  are  as  much  indebted 
for  the  experimental  development  of  the  subject  as  we 
are  to  Raoult  for  its  theoretical.  That  one,  which, 
judged  by  the  results,2  seems  to  be  on  the  whole,  the 
most  satisfactory,  is  seen  in  Fig.  6.  The  inner  glass 
vessel  A,  provided  with  a  return  condenser  K,  receives 
the  liquid  whose  boiling-point  is  to  be  determined. 
The  bottom  of  this  vessel  is  filled  to  a  depth  of  a 
few  centimeters  with  glass  beads  or  small  garnets,  so 
that  the  boiling  may  take  place  from  a  number  of  points 
and  proceed  more  smoothly.  The  bulb  of  the  Beckmann 
thermometer  is  placed  well  below  the  surface  of  the 
liquid.  Tube  A  is  surrounded  on  the  sides  with  a  double- 
walled  glass  jacket  B,  into  which  some  of  the  same  sol- 
vent placed  in  A  is  poured.  The  object  is  to  surround 
the  boiling  liquid  with  a  liquid  as  nearly  at  its  own  tem- 
perature as  possible.  This  jacket  is  provided  with  a 
return  condenser  Ka.  The  whole  is  supported  on  a  box 

1  Ztschr.  phys.  Chem.,  4,  544  ;  8,  224  ;  15,  663  ;  21,  246. 
a  Ibid,  8,  224. 


THE   BOIUNG-POINT   METHOD 


of  asbestos  C,  which  is  open  beneath, 
as  shown  in  the  drawing. 


Heat  is  applied 


Fig.  6. 

The  results  obtained  by  Beckmann1  with  the  use  of 
this  apparatus  were  very  good.  It  is,  however,  not  free 
from  objections.  It  is  a  question  whether  the  effect  of 
radiation  from  the  bulb  of  the  thermometer  outward  upon 
the  colder  objects,  was  entirely  cut  off  by  the  form  of 

i  Ztschr.  phys.  Chem.,  8,  226. 


THE   BOILING-POINT   METHOD  33 

jacket  employed.  Beckmann1  used  in  a  later  form  a 
porcelain  jacket,  having  abandoned  a  metallic  one, 
which  doubtless  cut  off  the  radiation  more  effectively 
than  the  one  of  glass.  But  an  objection  which  applies 
to  every  form  devised  by  Beckmann,  is  that  the  cold 
solvent  from  the  condenser  is  returned  directly  into  the 
hot  liquid  in  which  the  thermometer  is  immersed.  That 
the  thermometer  is  affected  by  this,  in  that  it  tends  to 
lag  behind  the  true  boiling-temperature  of  the  liquid,  is 
probable. 

A  form  of  apparatus  which  largely  eliminates  this 
latter  source  of  error,  was  devised  by  Hite,2  and  is 
shown  in  Fig.  7.  The  distinctive  advance  made  by 
Hite  is  the  introduction  of  an  inner  glass  tube,  which 
prevents  the  condensed  solvent  from  coming  in  contact 
with  the  thermometer  before  it  is  reheated  to  the  boil- 
ing-point. The  cooled  liquid  must  pass  through  a  layer 
of  the  boiling  liquid  between  the  walls  of  the  inner  and 
outer  vessel,  some  centimeters  deep,  before  it  can  enter 
the  inner  tube  which  receives  the  thermometer.  The 
inner  vessel  is  closed  at  the  bottom  by  means  of  a  glass 
stopper.  Grooves  are  filed  into  the  edge  of  the  stop- 
per to  allow  the  vapor  to  stream  through  into  the  inner 
vessel  in  fine  bubbles,  and  stir  the  liquid  around  the 
thermometer.  I  am  inclined  to  lay  rather  less  stress 
upon  the  importance  of  this  device,  than  upon  the 
separation  of  the  condensed  solvent  from  the  liquid  in 
which  the  thermometer  is  placed,  until  it  has  been  re- 
heated to  the  boiling-point.  The  apparatus  gave  ad- 
mirable results  with  low-boiling  solvents,  but  could  not 
be  used  for  solvents  which  boil  over  100°. 

The  present  writer"  has  devised  a  form  of  apparatus 

1  Ztschr.  phys.  Chem.,  15,  662. 

2  Am.  Chem.  J.,  17,  514. 
8/fo'rf,  19,  581. 


34  THE   BOIUNG-POINT   METHOD 

which  aims  both  at  reducing  the  error  from  radiation  to 
a  minimum,  and  at  preventing  the  condensed  solvent 
from  coming  in  contact  with  the  thermometer  until  it  is 
reheated  to  the  boiling-point.  It  is  also  one  of  the  sim- 
plest of  the  efficient  forms  thus  far  devised.  It  is  shown  in 
section  in  Fig.  8.  A  is  a  glass  tube  18  cm.  high  and  4 
cm.  in  diameter,  drawn  out  at  the  top  to  a  diameter  of 
about  2f  cm.  and  ground  to  receive  a  ground-glass  stop- 
per. This  tube  is  filled  to  a  depth  of  from  3  to  4  cm. 
with  glass  beads.  P  is  a  cylinder  of  platinum,  8  cm. 
high  and  2^  cm.  in  width,  made  by  rolling  up  a  piece  of 
platinum  foil,  and  fastening  it  in  position  by  wrapping  it 
near  the  top  and  bottom  with  platinum  wire.  Into  the 
cylinder  P,  some  pieces  of  platinum  foil  are  thrown. 
These  are  made  by  cutting  foil  into  pieces  about  f  cm. 
square,  bending  the  corners  alternately  up  and  down,  to 
prevent  them  from  lying  too  closely  upon  one  another, 
and  serrating  the  edges  with  scissors,  to  give  a  greater 
number  of  points  from  which  the  boiling  can  take  place. 
The  bulb  of  the  thermometer  is  thus  entirely  surrounded 
by  metal  at  very  nearly  its  own  temperature,  except 
directly  above.  A  condenser  C,  about  40  cm.  in  length, 
is  attached  to  the  tube  A,,  which  is  2  or  2jcrn.  in  diame- 
ter, by  means  of  a  cork.  When  it  is  desired  to  protect 
the  solvent  from  the  moisture  in  the  air,  the  top  of  the 
condenser  tube  should  be  provided  with  a  tube  contain- 
ing calcium  chloride  or  phosphorus  pentoxide.  During 
an  experiment,  the  vessel  A  is  closed  above  by  a  cork, 
through  which  the  Beckmann  boiling-point  thermometer 
T  passes.  M  is  a  jacket  of  asbestos,  12  cm.  high  and 
ij  cm.  thick,  over  the  top  of  which  the  rate  of  boiling 
can  be  observed  satisfactorily.  It  is  constructed  by 
bending  a  thin  board  of  asbestos  tightly  around  the 
tube  A,  and  fixing  it  in  place  by  means  of  a  copper 


Fig.  7. 


Fig.  8. 


36  THU  BOILING-POINT  METHOD 

wire.  Thick  asbestos  paper  is  then  wound  around  this 
until  the  desired  thickness  is  reached.  The  apparatus 
is  supported  on  a  small  iron  tripod  S,  8  cm.  in  diameter, 
on  which  rests  an  asbestos  ring  R,  about  9  cm.  in  exter- 
nal diameter.  A  circular  hole  is  cut  in  the  center  of 
this  ring,  about  3^-  cm.  in  diameter,  and  over  this  is 
placed  a  piece  of  fine  copper  gauze.  The  source  of  heat 
is  a  Bunsen  burner  B,  surrounded  by  an  ordinary 
metallic  cone  I,  to  protect  the  small  flame  from  air- 
currents.  The  glass  vessel  A  is  shoved  down  until  it 
comes  in  contact  with  the  wire  gauze.  Under  these  con- 
ditions a  very  small  flame  suffices  when  low-boiling  sol- 
vents are  employed,  and  not  a  large  flame  is  required 
when  a  solvent  like  aniline  is  used. 

A  number  of  other  forms  of  apparatus  have  been  con- 
structed for  determining  the  boiling-points  of  liquids, 
but  these  either  do  not  eliminate  error  sufficiently  for 
accurate  work,  or  are  so  complex  that  they  can  scarcely 
hope  to  find  general  application  in  the  laboratory  for 
the  purpose  of  determining  molecular  weights. 

Carrying  Out  a  Determination 

The  thermometer  must  first  be  so  adjusted  that  the 
top  of  the  mercury  thread  comes  to  rest  on  the  lower 
half  of  the  scale,  when  the  bulb  is  immersed  in  the  boil- 
ing solvent.  This  is  accomplished  by  placing  some 
glass  beads  in  cylinder  A,  and  adding  the  pure  solvent 
until  the  bulb  of  the  thermometer  will  be  covered  when 
inserted  in  place.  The  solvent  is  then  boiled,  and  as 
much  mercury  as  possible  is  driven  out  of  the  lower  bulb 
into  the  upper  cup.  The  thermometer  is  then  removed 
from  the  liquid,  inverted  for  a  few  moments,  when  still 
more  of  the  mercury  in  the  bulb  will  run  down  into  the 
cup.  The  thermometer  is  then  quickly  brought  into 


THE   BOILING-POINT   METHOD  37 

normal  position  and  given  a  sudden  tap,  when  the  mer- 
cury will  fall  from  the  top  to  the  bottom  of  the  cup  and 
leave  the  column  free.  The  bulb  is  again  placed  in  the 
boiling  solvent,  and  if  the  thread  comes  to  rest  where  de- 
sired, the  apparatus  is  ready  for  a  determination.  If  not, 
the  process  must  be  repeated  until  the  desired  end  is 
reached,  which,  however,  does  not  usually  require  any 
considerable  expenditure  of  time. 

When  the  thermometer  is  adjusted,  it  must  be  re- 
moved, and  the  apparatus  and  beads  entirely  freed  from 
the  liquid.  The  glass  beads  are  then  poured  into  the 
glass  cylinder,  the  platinum  cylinder  inserted,  and 
pressed  down  into  the  beads  to  a  distance  of  from  £  to  i 
cm.  The  platinum  plates  are  then  introduced  into  the 
platinum  cylinder,  the  end  of  the  tube  A,  closed  with  a 
cork,  and  the  ground-glass  stopper  inserted  into  A. 
The  apparatus  is  then  set  into  a  small  beaker  glass  and 
weighed,  the  solvent  introduced,  and  the  whole  re- 
weighed.  /Great  care  must  be  taken  that  not  enough 
solvent  is  employed  to  boil  over  from  one  side  of  the 
platinum  cylinder  to  the  other. )  In  case  a  labora- 
tory is  not  provided  with  a  balance  capable  of  weighing 
accurately  200  or  300  grams,  the  solvent  must  be  weighed 
directly  and  poured  into  the  apparatus.  This  method  of 
procedure,  for  low-boiling  solvents,  is  necessarily  less  ac- 
curate, due  to  loss  by  evaporation. 

After  the  solvent  is  weighed,  the  glass  stopper  is  re- 
moved, and  the  thermometer,  fitted  tightly  into  a  cork,  is 
placed  in  position,  as  shown  in  the  drawing.  The  appa- 
ratus is  then  placed  upon  the  stand  in  the  mantle  of  asbes- 
tos, the  cork  removed  from  A,  and  the  condenser  at- 
tached. Heat  is  then  applied  and  the  solvent  boiled. 
The  size  of  the  flame  must  be  so  regulated  by  means  of 
a  screw  pinch- cock,  that  the  boiling  is  quite  vigorous, 


38  THE   BOIUNG-POINT   METHOD 

but  not  so  violent  as  to  be  of  an  irregular  or  explosive 
character.  A  quiet,  but  very  active  boiling  is  absolutely 
essential  to  the  success  of  the  experiment.  The  time 
required  to  establish  the  true  temperature  of  equilibrium 
between  the  pure  liquid  solvent  and  its  vapor,  is 
much  greater  than  in  the  case  of  a  solution^  This  is 
strictly  analogous  to  what  is  observed  with  the  freezing- 
point  method.  Here,  the  time  necessary  to  establish 
the  temperature  of  the  equilibrium  between  the  solid  and 
liquid  phases  of  the  pure  solvent,  is  always  much  greater 
than  for  a  solution.  Before  taking  a  reading  on  the 
Beckmann  thermometer,  it  is  always  necessary  to  give  if 
a  few  sharp  taps  with  a  lead  pencil,  and  indeed  this 
should  be  done  occasionally  while  the  mercury  is  rising, 
and  especially  when  it  is  near  the  point  of  equilibrium. 
The  use  of  an  electric  hammer  to  accomplish  this  object 
is  an  unnecessary  complication.  A  small  hand-lens, 
magnifying  a  half  dozen  times,  is  quite  sufficient  to  use 
in  making  the  readings.  It  is  always  best  to  redetermine 
the  boiling-point  of  the  solvent.  After  this  point  has  been 
ascertained,  a  tube  containing  the  substance  pressed  into 
pellets,  whose  molecular  weight  it  is  desired  to  determine, 
is  weighed,  and  a  convenient  number  of  these  poured 
into  the  solvent,  either  through  the  condenser,  or  directly 
through  the  tube  A  when  the  solvent  is  not  too  volatile, 
and  has  ceased  to  boil.  The  tube  is  then  reweighed, 
and  the  amount  of  substance  introduced,  thus  ascertained. 
The  boiling-point  of  the  solution  is  then  determined. 

The  carrying  out  of  a  determination  with  a  low-boil- 
ing solvent  is  a  much  easier  process  than  with  one  boil- 
ing at  a  considerably  higher  temperature. 

Thus  :  when  anisol  or  aniline  is  employed,  much  care 
and  some  experience  are  necessary  to  determine  the  rate 
of  boiling  which  must  be  adopted.  If  the  boiling  is  too 


THE   BOIUNG-POINT   METHOD  39 

slow,  the  thermometer  will  never  reach  the  temperature 
of  equilibrium  ;  if  so  rapid  that  it  is  irregular  and  explo- 
sive, the  thermometer  may  rise  above  the  true  point,  and 
then  suddenly  drop  below  it  at  the  moment  when  a  large 
amount  of  the  vapor  is  set  free.  In  a  word,  for  high- 
boiling  solvents,  the  rate  of  boiling  must  be  as  vigorous 
as  possible,  in  order  to  proceed  with  perfect  regu- 
larity. 

In  all  such  determinations  the  barometer  must  be 
carefully  observed  ;  but  after  the  boiling-point  of  the  sol- 
vent has  been  determined,  that  of  the  solution  can  be  as- 
certained so  quickly,  that  the  changes  in  the  barometer 
during  this  short  interval  are  usually  so  slight  that  they 
are  negligible.  Whenever  they  are  of  appreciable  value, 
a  correction  must  be  accordingly  introduced. 

A  portion  of  the  nearly  pure  solvent  is  constantly  be- 
ing evaporated  from  the  solution,  and  condensed  on  the 
walls  of  the  apparatus  itself,  and  in  the  condenser.  The 
solution  is  thus  more  concentrated  than  would  be  calcu- 
lated from  the  amount  of  substance  and  of  solvent  used. 
A  correction  must  be  introduced  for  the  amount  of  the 
solvent  which  separates  from  the  solution,  as  was  neces- 
sary for  the  freezing-point  method.  Unfortunately,  we 
cannot  determine  the  amount  in  the  boiling-point 
method  with  even  the  same  degree  of  accuracy  as  in  the 
freezing-point  method. 

The  amount  of  the  solvent  which  exists  as  vapor  and 
condensed  liquid,  is  given  by  Ostwald1  as  0.2  gram,  and 
0.35  gram  for  water.  But  this  evidently  holds  only 
under  a  special  set  of  conditions,  and  must  be  taken,  in 
general,  as  only  a  rough  approximation. 

Thus  all  the  data  are  at   hand   for  calculating  the 

1  Hand  und  Hilfsbuch  zur  Ausfiihrung  Physiko-Chemischer  Messungen, 
p.  224. 


40  THE   BOILING-POINT   METHOD 

molecular  weight  of  the  substance  in  the  solvent  used, 
from  the  formula  already  given  (page  28)  : 

Cw 


Below  are  given  a  few  of  the  results  obtained  with  my 
apparatus  for  solvents  boiling  from  34.  9°  to  182.5°. 

SOI/VENT,  ETHER  :  k  =  2110  ;  BOILING-POINT,  34.9°  AT  760  mm. 
Naphthalene,  128. 

FIRST  SERIES. 

Ether.        Naphthalene.         Rise  in          Molecular 
Grams.  Grams.        boiling-point.       weight. 

1  .........  57-573  1-2365  0-357°  126.9 

2  .........  57-573  2.5155  0.716°  128.8 

3  .........  57-573  3-8733  1.110°  127.9 

Mean,     127.9  % 

SOLVENT,  BENZENE  :  k  =  2670  ;  BOILING-POINT,  80.36°  AT 

760  mm. 
Naphthalene,  128.  f 

Benzene.      Naphthalene.        Rise  in  Molecular 

Grams.  Grams.       boiling-point.        weight. 

1  .........    70.560  0.7594  0.215°  133.7 

2  .........    70.560  2.0548  0.574°  135.4 

3  .........   70.560  3-0780  0.850°  137.0 

4  .........   70.560  44790  1.234°  137.4 

Mean,     135.9     >" 

SOLVENT,  ANILINE  :  k  =  3220  ;  BOILING-POINT,  182.5°  AT  738  mm. 
Triphenylmethane,  2441 

FIRST  SERIES. 

Aniline.  Triphenylmethane.  Rise  in  Molecular 

Grams.  Grams.         boiling-point.       weight. 

1  .........  60.126  0.8017  0.180°  238.6 

2  .........  60.126      1.6052      0-353°      243-5 

3  .........  60.126     2.2914     0.496°     247.4 

4  .........  60.126     2.9213     0.654°     239.2 

Mean,     242.2 


THE   BOILING-POINT   METHOD  41 

Diphenylamine ',  169. 

Aniline.  Triphenylmethane.  Rise  in  Molecular 

Grams.  Grams.        boiling-point.        weight. 

1 64.220  0.7780  0.224°  I74.I 

2 64.220  1.3326  0.391°  170.9 

3 64.220  1.7832  0.535°  l67-i 

Mean,     170.7 

For  practice  in  the  laboratory  it  is  far  better  to  use 
solvents  with  low  boiling-points,  such  as  ether  or  ben- 
zene. Ethyl  alcohol  can  be  employed,  but  with  it  the 
results  are  liable  to  be  less  accurate,  since  its  constant 
is  comparatively  small. 

Naphthalene  is  easily  obtained  pure,  and  may  be  used 
in  both  ether  and  benzene.  In  alcohol :  benzoic  acid, 
urea,  or  acetamide  may  be  conveniently  used ;  while  tri- 
phenylmethane,  diphenyl  amineor  benzanilide,  give  good 
results  with  aniline  as  a  solvent. 


PART  III 


THE  CONDUCTIVITY  METHOD 


Conductors  of  electricity  may,  for  the  sake  of  conve- 
nience, be  divided  into  two  classes,  those  which  conduct 
without  undergoing  any  decomposition,  such  as  the 
metals,  carbon,  etc.,  and  those  which,  during  the  passage 
of  the  current,  undergo  a  decomposition  or  electrolysis 
at  the  poles,  such  as  solutions  of  many  substances.  It 
is  not  at  all  certain  that  there  is  any  very  fundamental 
difference  between  the  two  classes,  and  at  present,  it 
seems  that  a  resemblance  between  the  two  modes  of  con- 
duction is  becoming  clearly  recognized. 

It  is  by  no  means  true  that  solutions  of  all  substances 
conduct.  Thus,  aqueous  solutions  of  the  so-called  neu- 
tsal  organic  compounds,  such  as  the  alcohols,  carbohy- 
drates, urea,  and  a  large  number  of  such  substances,  do 
not  conduct  the  current.  This  furnishes  ground  for  a 
division  of  substances  into  those  whose  solutions  con- 
duct and  are  called  electrolytes,  and  those  which,  in  solu- 
tion, do  hot  conduct  and  are  called  non-electrolytes. 

The  application  of  the  conductivity  method  in  phys- 
ical chemistry  is  limited  to  conductors  of  the  second 
class,  i.  e.,  to  solutions  of  electrolytes,  which  are  chiefly 
solutions  of  acids,  bases,  and  salts. 

The  conductivity  of  any  conductor  of  electricity  is  the 
reciprocal  of  its  resistance.  The  resistance  r  is,  from 
Ohm's  law,  expressed  thus  : 

7t 

i 


THK   CONDUCTIVITY   METHOD  43 

7t  is  the  difference  in  potential  at  the  two  ends  of  the 
conductor,  and  i  is  the  strength  of  current.  The  con- 
ductivity c  is  the  reciprocal  of  r. 

i 

7t 

The  unit  of  resistance,  called  the  ohm,  is  that  of  a  col- 
umn of  pure  mercury  106.3  cm.  long  and  i  square  mm. 
in  section,  at  o°  C. 

The  Siemens  or  mercury  unit  is  the  resistance  of  a 
column  of  mercury  100  cm.  in  length  and  with  a  cross 
section  of  one  square  mm.  The  two  units  bear  the  rela- 
tion to  one  another  of  106.3  :  100. 

Specific  and  Molecular  Conductivities 

The  resistance  of  conductors  depends  upon  their  form 
as  well  as  upon  their  chemical  nature.  In  order  that 
the  resistance  of  different  conductors  should  be  meas- 
ured in  comparable  quantities,  their  dimensions  must  be 
taken  into  account.  The  dimensions  usually  chosen  afe 
a  cylinder  i  meter  in  length  and  i  square  mm.  in  section. 
The  resistance  of  such  forms  of  conductors,  is  known  as 
their  specific  resistance.  The  reciprocal  of  this  is  their 
specific  conductivity.  f 

The  conductors  of  the  second  class  are  solutions 
of  some  electrolyte  in  some  solvent,  and  their  con- 
ductivity depends  chiefly  or  wholly  upon  the  presence 
of  the  electrolytic  substance.  That  the  resistances  of 
such  solutions  should  be  comparable,  it  is  clear  that  we 
must  deal  with  comparable  quantities  of  the  dissolved 
substances.  The  most  convenient  quantities  are  gram- 
molecular  weights. 

Given  a  normal  solution  which  contains  a  gram-molec- 
ular weight  of  the  electrolyte  in  a  liter.  If  this  liter  of 


44  THE   CONDUCTIVITY   METHOD 

solution  be  placed  between  two  electrodes  which  are  i 
cm.  apart,  the  cross  section  would  be  1,000  square  centi- 
meters. This  will  have  o.ooi  of  the  resistance,  or  1,000 
times  the  conductivity  of  a  cube  of  the  same  solution 
whose  edge  was  i  cm.  in  length.  If  we  represent  by  v 
the  number  of  cubic  centimeters  of  any  solution,  which 
contains  a  gram-molecular  weight  of  the  dissolved  sub- 
stance, and  by  s  the  specific  conductivity  of  a  cube  of 
the  solution  whose  edge  is  i  cm.  in  length,  the  molecu- 
lar conductivity  jw  is  the  product  of  these  quantities  : 

fii  =  vs. 

But  if  we  represent  by  s  the  specific  conductivity  of  a 
cylinder  of  the  solution  i  meter  in  length  and  i  square 
mm.  in  cross  section : 

>u  =  10,000  vs. 

A  general  expression,  where g  gram-molecular  weights 
are  contained  in  a  liter  of  the  solution,  is  : 

j  X  io3 

\JL  ' — 


g 

when  s,  the  specific  conductivity,  is  referred  to  a  cube 
of  the  solution,  or  : 


;*  = 


g 

when  5  is    referred    to  a  cylinder   of  the   solution,   i 
meter  in  length  and  a  square  mm.  in  cross  section. 

The  molecular  conductivities  of  solutions  are  then  the 
conductivities  of  comparable  quantities  of  different  sub- 
stances, and  when  the  same  dilutions  are  used,  the 
molecular  conductivities  are  directly  comparable  with 
one  another. 

Different  substances  behave  very  differently  with  re- 


THE   CONDUCTIVITY   METHOD  45 

spect  to  their  power  to  carry  the  current,  when  in  solu- 
tion in  a  given  solvent.  The  fundamental  distinction 
between  substances  which  conduct,  and  those  which  do 
not  conduct  at  all,  has  been  already  mentioned.  But 
among  conductors  very  marked  differences  exist.  Some 
reach  a  maximum  of  conductivity  at  moderate  dilution, 
while  others  attain  this  only  at  extreme  dilution. 
Take  the  case  of  a  strong  acid  like  hydrochloric  or 
nitric ;  the  molecular  conductivity  increases  with  the  di- 
lution to  about  one  one-thousandth  normal,  when  it  be- 
comes constant.  While,  on  the  other  hand,  the  molecu- 
lar conductivity  of  a  weak  acid  like  acetic,  will  increase 
with  the  dilution,  as  far  as  the  dilution  can  be  carried 
with  the  conductivity  method. 

The  question  arises,  whence  this  difference  between 
substances  in  respect  to  their  power  to  carry  the  cur- 
rent? Here  again,  the  theory  of  electrolytic  disso- 
ciation comes  to  our  aid.  Those  substances  which 
give  abnormally  great  depressidns  of  the  freezing-point, 
abnormally  large  elevations  of  the  boiling-point,  and 
which  show  abnormally  great  osmotic  pressures,  con- 
duct the  current ;  and  only  such  substances  conduct. 

The  explanation  of  the  abnormal  results  with  respect 
to  the  properties  just  mentioned,  was  sought  in  the  dis- 
sociation of  the  molecules  into  ions.  From  a  large 
amount  of  evidence  from  many  sources,  we  seem  justi- 
fied in  concluding  that  only  ions  conduct  the  current. 
Molecules  are  entirely  incapable  of  carrying  electricity 
through  the  solvent  in  which  they  are  dissolved.  If 
only  ions  conduct,  then  the  conductivity  of  a  solution  is 
proportional  to  the  number  of  ions  present,  provided 
that  the  ions  move  with  the  same  average  velocity, 
which  is  true  of  ions  of  the  same  kind. 

The  conductivity  method  can  then  be  used  to  meas- 


46  THE   CONDUCTIVITY   METHOD 

ure  the  dissociation  of  electrolytes  in  solution,  and  this 
is  its  most  important  scientific  application.  When  the 
molecular  conductivity  attains  a  maximum  constant 
value,  it  means  that  the  dissociation  is  complete,  and 
this  value  of  the  molecular  conductivity  is  termed  fa , 
The  molecular  conductivity  at  any  dilution  is  written  /v 
in  which  v  is  the  volume  of  the  solution,  i.  <?.,  the  number 
of  liters  which  contains  a  gram-molecular  weight  of  the 
electrolyte.  The  percentage  of  dissociation  at  any  dilu- 
tion, or,  is  the  ratio  between  the  molecular  conductivity 
at  that  dilution,  and  the  molecular  conductivity  when 
the  dissociation  is  complete  : 

a=-*-. 

//oo 

In  order  to  determine  the  dissociation  of  an  electrolyte 
at  any  given  dilution,  by  means  of  the  conductivity 
method,  it  is  necessary  to  determine  the  molecular  con- 
ductivity, jiy,  at  that  dilution,  and  the  value  of  ^  for 
that  electrolyte,  when  the  value  of  a  can  be  calculated 
at  once. 

Determination  of  /*«> 

The  value  of  ^v  is  determined  directly  for  any  electro- 
lyte in  any  solvent,  by  means  of  the  conductivity 
method.  The  determination  of  ^  for  strongly  disso- 
ciated electrolytes  is  comparatively  simple.  The  value 
of  fa,  is  determined  at  a  given  dilution,  the  dilution  in- 
creased, the  molecular  conductivity  determined  at  the 
new  dilution,  and  this  continued  until  a  dilution  is 
reached,  which  is  so  great,  that  when  further  increased, 
the  value  of  fa  remains  the  same.  It  has  then  attained 
a  constant  maximum  value,  which  is  the  value  of  //«,. 
The  value  of  //<»  for  strong  acids  and  bases,  and  for 


THK    CONDUCTIVITY   METHOD  47 

salts,  is  usually  attained  at  a  dilution  between  v  =  500 
and  v  =  5000.  This  will  be  seen  from  the  following  ex- 
amples : 


Hydrochloric  acid. 

Potassium  hydroxide.      Potassium  chlori 

v. 

J*v  18°. 

v. 

/!„  18°. 

V. 

ft,  18°. 

2 

301 

2 

184.1 

2 

95-8 

32 

335 

20 

204.5 

2O 

108.3 

128 

34i 

100 

212.4 

100 

II4.7 

1000 

346 

500 

214.0 

IOOO 

II9-3 

1667 

344 

1000 

211.  1 

5000 

120.9 

A  large  number  of  substances,  such  as  the  organic 
acids  and  bases,  which  are  only  weakly  dissociated  at 
any  ordinary  dilution,  present  a  new  problem,  when  it 
is  desired  to  determine  their  maximum  molecular  con- 
ductivity. That  this  is  not  reached  at  dilutions  to 
which  the  conductivity  method  can  be  applied,  is  seen 
from  the  following  examples  : 

Acetic  acid.  Ammonia.1 

v.  fart*.  v.  /^i8°. 

2  1.9  2  1.2 

20  6.2  20  4.3 

ioo       13.2  100       9.2 

1000       38.0  1000       26.0 

5000  79.6  5000  50.0 

10000       99.5  loooo       61.0 

It  is  evident  from  these  results  that  the  value,  of  J4*> 
for  such  substances  cannot  be  determined  by  the  method 
given  for  strongly  dissociated  compounds.  The  dilution 
at  which  complete  dissociation  would  take  place  lies  far 
beyond  the  possibility  of  applying  the  conductivity 
method  directly. 

The  method  of  determining  the  value  of  /*«>  for  such 
substances  is  as  follows.  While  the  weak  organic  acids 
are  only  slightly  dissociated,  salts  of  these  acids  are 

1  Ammonia  is  taken,  since  work  on  the  substituted  ammonias  has  not  gen- 
erally been  carried  to  very  great  dilutions. 


48  TH£   CONDUCTIVITY   METHOD 

completely  dissociated  at  moderate  dilutions.  So  also, 
with  respect  to  the  weak  bases,  which,  at  ordinary  dilu- 
tions, are  only  slightly  dissociated  ;  their  salts  are  com- 
pletely dissociated  at  dilutions  which  lie  well  within  the 
range  of  the  conductivity  method.  Take  an  organic 
acid.  Its  sodium  salt  is  prepared,  and  the  value  of  /*«> 
for  this  salt  determined  ;  or  taking  an  organic  base,  the 
nitrate  of  the  base  is  used,  and  the  value  of  fa  for  the  ni- 
trate determined. 

It  remains  to  see  what  relation  exists  between  the 
value  of  //GO  for  the  sodium  salt  of  an  acid,  and  the  acid 
itself,  or  between  the  nitrate  of  a  base  and  the  base. 

Kohlrausch1  has  shown  that  the  value  of  /*«,  for  any 
compound  is  the  sum  of  two  constants,  the  one  depend- 
ing upon  the  cation,  the  other  upon  the  anion.  The 
value  of  /*oo  for  sodium  acetate  is  the  sum  of  two  con- 
stants, the  one  for  the  cation,  sodium,  and  the  other  for 
the  anion,  CH3COO.  If  the  constant  for  sodium  be 
subtracted,  the  remainder  is  the  constant  for  the  anion 
of  acetic  acid.  If  to  this  constant  the  constant  for  hy- 
drogen be  added,  we  have  the  value  of  /*«>  for  acetic 
acid  itself.  Exactly  the  same  line  of  reasoning  applies 
to  the  nitrate  of  the  base. 

The  constant  for  NO3  is  subtracted  from  //«>  for  the 
nitrate,  and  the  remainder  is  the  constant  for  the  cation 
of  the  base.  To  this  the  constant  for  hydroxyl  is  added, 
and  the  sum  is  the  value  of  //«>  for  the  base. 

The  value  of  the  constant  for  sodium  is  49.2  at  25°, 
and  of  hydrogen,  325  at  25°.  If  we  add  275.8  to  the 
value  of  /*«>  for  the  sodium  salt  of  an  acid,  we  have  the 
value  of  //«5  for  the  acid.  The  value  of  the  constant  for 
NO3,  at  the  same  temperature,  is  65.  i ,  and  for  (OH) ,  170. 

1  Wied.  Ann.,  6,  167. 


THE    CONDUCTIVITY   METHOD  49 

We  must,  therefore,  add  105  to  ^  for  the  nitrate  of  a 
base,  in  order  to  ascertain  //«  for  the  base  itself. 

It  is  thus  possible  to  determine  /*<»  for  compounds 
which  are  only  slightly  dissociated  at  ordinary  dilutions. 
Since  pv  can  always  be  determined  for  any  electrolyte, 
we  are  able  to  measure  the  dissociation  of  compounds, 
which,  even  in  water,  are  only  slightly  dissociated. 

The  application  of  the  conductivity  method  to  meas- 
ure the  exact  dissociation  in  solvents  other  than  water 
is  not  always  so  successful.  Water  exercises  the  strong- 
est dissociating  action  of  any  known  solvent.  The  ion- 
izing power  of  many  solvents  is  comparatively  so 
weak  that  it  is  impossible  to  determine  the  value  of  ^x 
for  electrolytes,  which  are  strongly  dissociated  by  water, 
by  the  direct  application  of  the  conductivity  method. 
In  such  cases,  it  is  possible  to  determine  the  dissociation 
only  approximately. 

The  general  applicability  of  any  method  to  measure 
electrolytic  dissociation  is  of  wide-reaching  significance. 
This  will  appear,  when  we  consider  that  man}''  chemical 
reactions  take  place  between  ions,  molecules  as  such  not 
coming  into  play.  The  chemical  activity  of  solutions  is 
then  a  function  of  the  dissociation,  and  since  conduc- 
tivity is  a  measure  of  dissociation,  there  is  a  close  rela- 
tion between  the  conductivity  of  solutions,  and  their 
power  to  react  chemically.  Indeed,  the  former  has  often 
been  used  to  measure  the  latter. 

In  this  connection  is  to  be  mentioned,  especially,  the 
work  of  Ostwald'  on  the  conductivity  of  the  organic 
acids,  from  which  he  calculated  their  dissociation  con- 
stants. Knowing  the  dissociation  constant,  the  chem- 
ical activity  of  the  acid  is  known.  The  work  of  Bredig2 

1  Ztschr.  phys.  Chem.,  3,  170,  241,369. 

2  Ibid,  13,  289. 


50  THE   CONDUCTIVITY   METHOD 

on  the  conductivity  of  organic  bases  is  strictly  analogous 
to  that  just  cited. 

Ostwald1  has  also  shown  that  it  is  possible  to  deter- 
mine the  basicity  of  acids  by  determining  the  conduc- 
tivity of  their  sodium  salts. 

The  conductivity  method  has  also  been  extensively 
applied  to  determine  what  we  have  already  called  the 
constants  for  the  ions,  or  the  relative  velocities  with 
which  the  ions  move  through  their  solutions. 

A  large  number  of  applications  of  the  conductivity 
method  to  special  problems  in  dissociation  have  been 
made  in  the  last  few  years,  so  that  it  may  be  said  to  be 
one  of  the  most  important  of  all  the  physical  chemical 
methods. 

The  Application  of  the  Conductivity  Method  to  the  Meas- 
urement of  Electrolytic  Dissociation 

When  a  continuous  current  is  passed  through  a  solu- 
tion of  an  electrolyte,  the  electrodes  become  quickly 
covered  with  gas,  or,  as  we  say,  become  polarized.  This 
increases  the  resistance  to  the  passage  of  the  current,  and 
interferes  with  the  measurement  of  the  resistance  of  the 
solution.  Several  devices  have  been  proposed  for  over- 
coming the  effect  of  polarization,2  but  none  have  proved 
as  simple  as  the  use  of  the  alternating  current. 
The  effect  of  polarization,  tending  to  retard  the  flow  of 
the  current  in  one  direction,  is  counterbalanced  by  the 
action  in  the  opposite  direction,  where  the  polarization 
current  adds  itself  to  the  original.  This  method  of 
measuring  the  conductivity  of  solutions  we  owe  to  Kohl- 
rausch. 

The  apparatus  employed  is  sketched  diagramatically 

1  Ztschr.  phys.  Chem.,  i,  105  ;  2,  902. 

2  Stroud  and  Henderson  ;  Phil.  Mag.,  43,  19. 


THE   CONDUCTIVITY   METHOD  51 

in  Fig.  9.  J  is  a  small  induction  coil,  with  only  one  or 
two  layers  of  wire.  A  larger  coil  must  not  be  used, 
since  it  does  not  give  a  sharp  tone  minimum  in  the  tele- 
phone. The  coil,  tuned  to  a  very  high  pitch,  should  be 
inclosed  in  a  box  surrounded  by  a  poor  conductor  of 


W 


sound,  and  placed  at  some  distance  from  the  bridge 
where  the  reading  is  to  be  made.  The  coil  is  driven  by  a 
storage  cell  of  medium  size.  A  platinum  wire,  or  bet- 
ter one  of  manganese  alloy,  which  has  a  small  tempera- 
ture coefficient  of  resistance,  is  tightly  stretched  over  the 
meter  stick  AB,  which  is  carefully  divided  into  millime- 
ters. A  rheostat  W,  whose  total  resistance  amounts  to 
1 1, 1 10  ohms,  is  convenient.  The  resistance  vessel  R, 
containing  the  solution  and  electrodes,  is  shown  enlarged 
in  Fig.  10.  The  electrodes  are  cut  from  thick  sheet 
platinum,  and  into  each  plate  a  stout  platinum  wire, 
about  an  inch  in  length,  is  welded.  Glass  tubes  are 
sealed  on  to  the  platinum  wires  and  electrode  plates,  by 
means  of  sealing  glass,  as  shown  in  the  drawing.  These 
tubes  pass  tightly  through  a  rubber  cap,  which  fits  over 
the  glass  vessel.  They  are  filled  to  a  convenient  height 
with  mercury,  and  electrical  connection  established  by 
means  of  copper  wires,  which  dip  into  the  mercury.  One 
arm  of  the  telephone  T  is  thrown  into  the  circuit  be- 


THE   CONDUCTIVITY   METHOD 


tween  the  rheostat  and  the  resistance,  and  the  other  arm 
is  connected  with  the  bridge  wire,  by  means  of  a  slider. 


Fig.  10. 

This  is  moved  along  the  wire  until  that  point  is  found  at 
which  the  hum  of  the  induction  coil  ceases  to  be  heard 
in  the  telephone.  I^et  this  be  some  point  c,  and  let  us 
represent  Ac  by  « ,  and  Br  by  b,  the  resistance  of  the  so- 
lution in  the  vessel  R  by  r,  and  the  resistance  in  ohms 
in  the  rheostat  by  w ;  then,  from  the  principle  of  the 
bridge,  we  have  : 

ra  =  wb. 
_  wb 
a  ' 


THE    CONDUCTIVITY   METHOD  53 

But  the  conductivity  of  a  solution  c  is  the  reciprocal  of 
the  resistance  r  ;  therefore, 

a 
c  —  —  7. 

wb 

The  conductivity  of  solutions,  determined  by  this  ex- 
pression, would  not,  in  any  sense,  be  comparable  with 
one  another,  since  there  is  nothing  in  the  expression 
which  takes  into  account  the  concentration  of  the  solu- 
tion. It  is  most  convenient  to  refer  all  concentrations  to 
the  molecular  normal,  containing  a  gram-molecular 
weight  of  the  electrolyte  in  a  liter.  If  we  represent  by 
i)  the  number  of  liters  which  contains  a  gram-molecular 
weight  of  the  dissolved  substance,  the  preceding  ex- 
pression becomes  : 

va 

c  =  —  7. 
wb 

Instead  of  the  conductivity  c,  we  write  for  the  molecu- 
lar conductivity,  /*,  and  to  indicate  the  concentration 
at  which  the  /*  is  determined,  we  write  //z/,  in  which  v 
has  the  significance  indicated  above. 

va 


But  even  this  expression  does  not  take  into  account  the 
dimensions  of  the  cell  used.  A  cell-constant  C  must  be 
introduced,  and  determined  for  each  cell,  before  it  can  be 
employed  for  conductivity  measurements.  The  com- 
plete expression  for  the  molecular  conductivity  is  then 


Temperature  Coefficient  of  Conductivity 

The  conductivity  of  solutions  of  electrolytes  increases 
rapidly  with  rise  in  temperature.  The  molecular  con- 
ductivity of  a  solution  of  hydrochloric  acid,  which  is 
301.7  at  18°,  rises  to  331  at  25°.  This  is  even  more 
marked  in  the  case  of  sodium  sulphate  ;  a  solution  hav- 
ing a  conductivity  of  94.8  at  18°  has  a  conductivity  of 
171.4  at  50.3°,  of  252  at  82°,  and  of  286.4  at  99.4°. 

From  this  it  is  evident,  that  a  definite,  constant  tern- 


Fig,  ii. 

perature  must  be  carefully  maintained  in  conductivity 
work.  This  is  accomplished  by  placing  the  vessel  con- 
taining the  solution  in  a  large  volume  of  water,  which  is 
maintained  at  a  constant,  known  temperature.  A  con- 
venient form  of  thermostat  (Fig.  n)  for  such  work  has 
been  devised  by  Ostwald.1  A  metallic  vessel,  containing 
from  15  to  20  liters  of  water,  is  stirred  by  paddles  driven 

1  Ztschr.  phys.  Chem.,  a,  565. 


THK   CONDUCTIVITY   METHOD 


55 


by  a  fan,  which  is  kept  in  motion  by  means  of  a  small 
gas  jet  beneath.  The  tube  near  the  bottom  of  the  large 
vessel  is  filled  with  a  10  per  cent,  solution  of  calcium 
chloride.  The  change  in  volume  of  this  solution  with 
the  temperature,  is  used  to  regulate  the  temperature  of 
the  water-bath. 

The  Ostwald  regulator  (Fig.  12)  can  be  easily  ad- 
justed, so  that  the  temperature  of  the  water-bath  will  re- 
main constant,  to  within  one-tenth  of  a  degree,  fora  day. 
Tube  A  is  connected  with  the  gas  supply.  The  glass 
tube  C,  which  opens  just  above  the  mercury  meniscus, 


Fig.  12. 

contains  a  fine  perforation  in  the  side,  so  as  to  supply 
gas  enough  to  keep  the  flame  alive,  when  the  lower  end 
of  the  tube  is  closed  by  the  mercury.  Tube  B  connects 
with  the  burner,  and  D  with  the  large  tube  containing  the 
calcium  chloride  solution,  resting  on  the  bottom  of  the 
water-bath. 

When  it  is  desired  to  adjust  the  regulator  for  a  defi- 
nite temperature,  the  stop-cock  is  opened,  the  flame 
lighted,  and  a  thermometer,  divided  into  tenths  of  a  de- 
gree, suspended  in  the  bath.  The  end  of  tube  C  is 
raised  above  the  mercury  surface,  and  the  stirrer  is  set 
in  motion  by  means  of  the  small  gas  jet,  placed  about  a 


56  THK    CONDUCTIVITY   METHOD 

foot  below  the  fans.  When  the  thermometer  registers 
the  desired  temperature,  the  stop-cock  is  closed,  and  the 
end  of  tube  C  is  pushed  down  until  it  just  touches  the 
mercury  surface.  The  apparatus  will  then  control  the 
temperature  automatically. 

Calibrating  the  Wire 

A  stout  platinum  wire  can  be  used  in  constructing  the 
Wheatstone  bridge,  but,  as  already  stated,  it  is  better  to 
use  one  of  an  alloy  of  manganese  (mangandraht) .  This 
wire  is  usually  of  very  nearly  uniform  resistance,  but 
this  can  never  be  taken  for  granted  without  testing  it. 
A  convenient  method  for  calibrating  such  a  wire  has 
been  described  by  Strouhal  and  Barus.1  A  piece  of 
German-silver  wire  about  a  meter  and  a  half  in  length, 
is  cut  into  ten  pieces  (Fig.  13),  which  are,  as  nearly  as 


Fig-  13- 

possible,  of  the  same  length.  The  insulation  is  removed 
from  the  ends  of  these  wires,  and  they  are  soldered  on  to 
thick  copper  wires  about  an  inch  in  length.  Nine  holes 
are  made  in  a  board,  which  is  about  a  meter  in  length, 
at  equal  distances  apart.  These  are  partly  filled  with 
mercury,  and  receive  the  ends  of  the  copper  wires,  which 
have  been  previously  amalgamated.  The  board,  with 
the  wires  in  position,  is  placed  along  by  the  side  of  the 
bridge  wire,  and  the  two  end  loops  attached  to  the  ex- 
tremities of  the  bridge.  The  current  from  the  small  in- 
ductorium  is  passed  through  the  bridge,  and  also 

1  Wied.  Annalen,  10,  326. 


THK   CONDUCTIVITY   METHOD  57 

through  the  series  of  loops.  One  of  the  loops  is  chosen 
as  the  standard  of  measure,  and  is  suitably  marked 
so  as  to  distinguish  it  from  the  others.  One  end  of  this 
standard  is  attached  to  one  end  of  the  bridge,  and  the 
other  placed  in  the  first  mercury  cup.  One  arm  of  the 
telephone  is  placed  in  the  same  mercury  cup,  and  the 
other  attached  to  the  pointer,  which  moves  along  the 
bridge  wire.  The  point  of  silence  on  the  bridge  is  as- 
certained. This  is  the  first  reading  for  point  i.  The 
telephone  and  all  other  connections  remaining  un- 
changed, the  standard  measuring  wire,  which  was  at 
position  i,  is  moved  to  position  2,  and  wire  2  is  placed 
in  position  i.  A  reading  is  again  made  in  the  tele- 
phone, which  is  the  second  reading  for  position  i.  The 
arm  of  the  telephone,  which  was  in  cup  i,  is  then  re- 
moved to  cup  2,  and  the  point  of  silence  ascertained. 
This  is  the  first  reading  for  cup  2.  The  standard  wire, 
which  is  now  in  position  2,  is  moved  to  position  3,  wire  3 
is  taken  back  to  2,  and  all  other  connections  are  un- 
changed. The  point  of  equilibrium  is  again  ascertained 
at  2,  which  gives  the  second  reading  for  this  position. 
The  standard  wire  is  thus  interchanged  in  position  with 
each  of  the  loops,  and  two  readings  obtained  on  the 
bridge  for  each  position  except  the  last,  for  which  only 
one  reading  is  available. 

It  must  be  observed  that  in  all  such  work  in  which  the 
telephone  is  used  it  is  not  advisable  to  try  to  ascertain 
directly,  the  exact  point  on  the  wire  at  which  the  coil 
cannot  be  heard,  or  at  which  the  tone  is  a  minimum  ; 
but  to  find  a  point  on  each  side  of  the  true  zero,  at  which 
the  intensity  of  the  tone  is  the  same.  These  two  read- 
ings should,  at  most,  be  not  more  than  a  centimeter 
apart.  The  true  zero  is  then  just  half-way  between 
these  points. 


58  THE   CONDUCTIVITY   METHOD 

The  bridge  wire  is  thus  divided  into  ten  lengths.  The 
application  of  the  calibration  correction  is  simple.  The 
ten  values  are  added  together,  and  their  sum  subtracted 
from  1,000  mm.  The  difference  is  divided  into  10  parts 
and  each  length  is  corrected  by  this  amount,  so  that  the 
sum  is  1,000  mm.  By  adding  the  parts  thus,  i,  1  +  2, 
etc.,  we  obtain  the  points  which  correspond  to  tenths  of 
the  wire.  The  difference  between  these  and  10,  20,  etc., 
gives  the  correction  to  be  applied. 

Carrying:  Out  a  Conductivity  Measurement 

After  the  wire  is  calibrated,  the  next  step  is  to  deter- 
mine the  value  of  the  constant  (C),  for  the  cell  which  is 
to  be  used.  The  preparation  of  the  cell  is  a  matter  of 
some  care.  In  the  first  place,  the  electrodes  must  be 
placed  at  a  convenient  distance  apart,  by  shoving  the 
glass  tubes  through  the  ebonite  cover,  and  these  must 
then  be  fastened  firmly  in  the  rubber  plate,  so  that  no 
further  movement  is  possible.  If  a  fairly  concentrated 
solution  is  to  be  studied,  the  plates  must  be  as  much  as 
2,  or  2.5  cm.  apart.  If  a  very  dilute  solution  is  to  be 
used,  a  distance  of  0.5  cm.  is  sufficient.  The  ordinary 
white  platinum  plates,  such  as  are  furnished  by  the  manu- 
facturers, cannot  be  used  directly,  since  they  would  not 
give  a  sharp  tone-minimum  in  the  telephone.  They 
must  be  carefully  cleansed  by  washing  in  chromic  acid, 
and  then  in  water.  A  few  drops  of  a  solution  of  pla- 
tinic  chloride  are  poured  into  the  conductivity  cell,  (Fig. 
10)  and  the  cell  filled  with  pure  water  until  the  electrodes 
are  covered.  A  current  from  a  storage  battery  is  then 
passed  through  the  solution  until  the  electrodes  become 
more  and  more  deeply  blackened.  The  direction  of  the 
current  should  be  frequently  altered,  so  that  both  elec- 
trodes may  become  coated,  and  that  the  deposit  may  be 


THE    CONDUCTIVITY   METHOD  59 

as  uniform  as  possible.  After  the  plates  are  completely 
covered  with  a  layer  of  the  platinum  black,  the  platinic 
chloride  is  removed  from  the  cell,  a  little  sodium  hydrox- 
ide added,  and  the  current  passed  through  this  solution. 
The  object  of  the  alkali  is  to  remove  any  chlorine  which 
may  have  been  retained  by  the  platinum  black  as  it  was 
being  deposited.  The  sodium  hydroxide  is  then  re- 
moved by  hydrochloric  acid,  and  the  acid,  by  repeated 
washing  with  pure  redistilled  water. 

In  order  to  determine  the  value  of  C,  in  the  expression 

~  va 


for  any  cell,  it  is  necessary  to  use  some  solution  for 
which  the  value  of  //„  is  known.  Since  potassium  chlo- 
ride can  generally  be  obtained  in  a  high  degree  of  purity, 
by  five  or  six  crystallizations,  it  is  convenient  to 
use  in  standardizing  the  cell.  A  one-fiftieth  normal  solu- 
tion of  potassium  chloride  has  a  molecular  conductivity 
(/*«,)  of  129.7  at  25°  C.  The  solution  is  poured  into  the 
cell  until  the  electrodes  are  covered,  and  brought  to  ex- 
actly 25°  C.  in  the  thermostat.  The  bubbles  of  air 
which  usually  separate  on  the  electrodes  with  rise  in 
temperature,  having  been  removed,  a  resistance  is  thrown 
into  the  circuit  by  means  of  the  rheostat,  which  will 
bring  the  point  of  tone-minimum  not  very  distant  from 
the  center  of  the  bridge,  say  between  400  and  600  mm. 
Thus  all  the  quantities  in  the  above  expression,  except 
C,  are  known,  and  it  can  therefore  be  solved  at  once  for 
the  value  of  C. 

The  constant  for  any  given  cell  being  determined,  it  is  a 
matter  of  fundamental  importance  that  its  value  should  not 
be  changed.  This  would  be  done  if  the  electrodes  were 
moved  with  respect  to  one  another,  or  their  surfaces  in 


60  THK   CONDUCTIVITY   METHOD 

any  wise  altered.  It  is  therefore  necessary  that  the 
electrodes  should  never  be  placed  upon  a  hard  surface, 
but  always  upon  clean,  thick,  filter  paper,  and  the  plates 
must  never  be  touched  with  any  hard  object. 

Knowing  the  constant  for  the  cell,  the  measurement 
of  the  conductivity  of  a  solution  involves  exactly  the 
same  procedure  as  that  just  described.  The  difference 
is  in  the  calculation.  C  is  known,  and  it  is  desired  to 
find  the  value  of  /*»  for  a  given  solution. 

The  solution  is  placed  in  the  cell,  brought  to  25°  C., 
the  resistance  introduced  in  the  rheostat,  and  the  bal- 
ance effected  on  the  bridge.  All  the  values  in  the  above 
expression  are  now  known  except  }*Vl  which  is  calcu- 
lated directly. 

If  the  solution  used  is  more  concentrated  than  j^- 
normal,  it  is  better  to  use  the  cell  whose  electrodes  are 
far  apart.  If  more  dilute,  the  electrodes  whose  dis- 
tance from  one  another  is  not  more  than  0.5  cm.  should 
be  employed. 

Precautions  are  necessary  at  every  turn.  The  wire, 
after  calibration,  must  never  be  touched  with  the  hand, 
and  the  point  of  contact  with  the  wire  must  be  moved 
over  its  surface  very  carefully.  The  current  must  not 
be  allowed  to  flow  through  the  resistance  coils  for  any 
considerable  length  of  time,  or  the  temperature,  and 
therefore  the  resistance  of  the  coils  will  change.  The 
inductorium  should  be  allowed  to  run  only  during  the  ac- 
tual measurement  of  the  resistance.  Especial  care  should 
be  taken  that  every  connection  is  clean  and  well  made, 
otherwise  resistance  will  be  introduced  at  the  junctions. 

Correction  for  the  Conductivity  of  Water 

Since  water  is  the  most  general  solvent  known,  and 
solutions  in  this  solvent  have  the  greatest  conductivity, 


THE   CONDUCTIVITY   METHOD  6 1 

one  is  called  upon,  most  frequently  to  measure  the  conduc- 
tivity of  aqueous  solutions.  In  all  such  cases  the  quan- 
tity actually  measured  is  the  sum  of  the  conductivities 
of  the  water  and  of  the  dissolved  electrolyte.  The  con- 
ductivity of  the  water  alone,  must,  in  every  case,  be  de- 
termined, in  order  that  the  conducting  power  of  the 
electrolyte  may  be  ascertained.  It  would,  at  first  sight, 
appear  to  be  possible  to  use  water  of  only  a  fair  degree 
of  purity,  to  determine  its  conductivity,  and  then  to  sub- 
tract this  from  the  conductivity  of  the  solution.  Whether 
this  could  be  done,  would  depend  upon  the  nature  of 
the  impurities. 

They  might  easily  be  of  such  a  character  as  to  react 
chemically  with  the  dissolved  electrolyte,  and  thus  seri- 
ously affect  the  nature  of  the  solution.  Thus,  ammonia, 
which  would  neutralize  any  acid,  forming  a  salt,  would 
materially  change  the  nature  of  the  ions  present,  and 
therefore  the  conductivity.  Carbon  dioxide  would,  in 
like  manner,  affect  the  conductivity  of  any  strong  base. 
It  is  therefore  necessary,  in  all  work  involving  the  use  of 
the  conductivity  method,  to  prepare  water  in  as  pure  con- 
dition as  is  practicable,  and  then  to  introduce  a  correc- 
tion for  its  conductivity,  when  this  is  larger  than  the 
necessary  experimental  error. 

Kohlrausch1  has  prepared  the  purest  water  thus  far 
obtained,  by  distilling  the  purest  water  obtainable  by 
other  methods,  in  a  vacuum.  He  determined  its  con- 
ductivity without  exposure  to  the  air,  and  found  it  to  be 
0.04  X  10  ~6.  To  prepare  water  of  this  degree  of  purity 
is  not  practicable,  and  indeed  is  not  necessary  for  con- 
ductivity work. 

Nernst2  has  suggested  fractional  crystallization  as  a 

1  Ztschr.  phys.  Chem.,  14,  317. 
,  8,  120. 


62 


THE   CONDUCTIVITY   METHOD 


means  of  purifying  water  for  conductivity  purposes,  but 
equally  efficient  and  far  more  rapid  methods  have  been 
subsequently  devised. 

Hulett1  has  obtained  water  of  a  high  degree  of  purity, 
by  distilling  it  first  from  potassium  bichromate  and  sul- 
phuric acid,  and  then  redistilling  from  a  solution  of 
barium  hydroxide.  The  water  purified  in  this  way  had 
a  conductivity  of  from  0.7  to  0.8  X  io~ 6. 

More  recently,  Jones  and  Mackay2  have  used  an  appa- 
ratus in  which  the  water  is  distilled  first  from  acid 
potassium  permanganate  or  acid  potassium  bichro- 
mate, which  decomposes  any  organic  matter  present 
and  retains  the  ammonia,  and  second  from  alka- 
line potassium  permanganate,  which  retains  any  carbon 
dioxide.  The  apparatus  is  shown  in  Fig.  14.  Ordinary 


Fig.  14. 

distilled  water  is  introduced  into  the  vessel  A,  together 
with  a  little  sulphuric  acid  and  potassium  per- 
manganate, or  potassium  bichromate,  through  the 

1  Ztschr.  phys.  Chem.,  21,  297. 

2  Am.  Chem.  J.,  19,  91 ;  Ztschr.  phys.  Chem.,  aa,  237. 


THK   CONDUCTIVITY   METHOD  63 

funnel  tube  G.  It  is  heated  to  boiling,  the  vapor 
passing  into  B,  which  contains  distilled  water,  potas- 
sium permanganate,  and  a  little  potassium  or  sodium 
hydroxide.  A  small  flame  is  sufficient  to  keep  the  liquid 
in  B  at  the  boiling  temperature.  The  vapor  passes  from 
B  along  the  long  neck  of  the  retort,  over  the  glass  wool, 
which  is  meant  to  arrest  any  trace  of  permanganate  car- 
ried along  by  the  steam,  into  the  tin  condenser,  and  is 
received  in  the  flask  E.  Certain  precautions  must  be 
taken  in  fitting  up  and  using  the  apparatus.  The  glass 
wool  W,  introduced  into  the  adapter  arm  C,  must  fill 
only  the  lower  part  of  the  arm,  otherwise  there  is  dan- 
ger that  a  trace  of  alkali  dissolved  from  it,  will  be  swept 
over  into  the  condenser.  The  glass  wool  should  be 
washed  well  with  hydrochloric  acid.  Whenever  the  ap- 
paratus is  cleaned  and  refilled,  which  should  be  done 
about  once  a  week  when  in  constant  use,  the  distillate 
collected  at  first,  must  be  discarded,  since  it  always  con- 
tains a  trace  of  alkali,  probably  of  ammonia,  formed  by 
the  action  of  the  alkaline  permanganate  on  the  organic 
impurities  in  the  ordinary  distilled  water  introduced  into 
B.  When  this  is  once  removed,  there  is  no  further 
escape  of  ammonia  possible,  since  the  organic  impuri- 
ties in  the  water  are  destroyed  by  the  permanganic  acid 
in  A,  and  the  ammonia  combines  with  the  sulphuric 
acid  present  in  that  vessel.  The  carbon  dioxide  liber- 
%ated  in  A,  is  absorbed  by  the  alkali  in  B.  The  process 
is  thus  perfectly  continuous  for  at  least  a  week,  or  it  can 
be  interrupted  at  any  time,  by  removing  the  burner. 
Four  or  five  liters  of  water  can  be  obtained  daily  with  the 
use  of  this  apparatus. 

The  water  purified  by  this  method  gave  a  conductivity 
at  25°,  varying  from  1.5  to  2.0  X  ic"6  in  mercury  units. 

The  correction  which  must  be  applied  to  the  values  of 


64  THE   CONDUCTIVITY   METHOD 

/*z,,  for  the  conductivity  of  the  water  employed  in  pre- 
paring the  solutions,  is  calculated  by  multiplying  the 
specific  conductivity  of  the  water  by  the  molecular  vol- 
ume of  the  solution  in  cubic  centimeters.  This  quantity, 
for  water  properly  purified,  is  negligible  for  all  ordinary 
concentrations,  and  attains  an  appreciable  value  only  in 
dilute  solutions.  In  case  the  substance  under  investi- 
gation reacts  chemically  with  the  impurities  in  the  water, 
such  a  correction  would  be  so  uncertain  that  it  is  better 
not  to  attempt  to  apply  it. 

Substances  to  be  Used 

In  practice,  it  is  well  to  use  some  of  the  same  sub- 
stances whose  freezing-point  lowerings  have  been  meas- 
ured, that  the  dissociation  as  determined  by  conductivity, 
may  be  compared  with  that  calculated  from  the  depres- 
sion of  the  freezing-point.  Prepare  say  a  tenth-normal 
solution  of  the  substance  chosen,  determine  the  value  of 
pv  for  this  dilution,  increase  the  dilution  to  3-^-,  -5-^-, 
rcinr>  oT5inr>  an<*  T7mnrnormal,  determining  in  each 
case  the  value  of  /v  At  about  -nnnr>  J*v  will  become 
constant,  and  will  show  no  further  increase  with  increase 
in  dilution.  This  is  the  value  of  /*<» .  To  find  the  per- 
centage of  dissociation,  <*,  at  any  dilution,  divide  the 
value  of  fa  at  that  dilution,  by  the  value  of  //«  for  the 
substance. 


a  = 


UNIVERSITY  OF  CALIFORNIA  LIBRARY 
BERKELEY 

Return  to  desk  from  which  borrowed. 
This  book  is  DUE  on  the  last  date  stamped  below. 


8    1947 
26Mar'58j  N 


LD  21-100m-9,'47(A5702sl6)476 


YC  21607 


oil 


'7* 


